diff --git a/src/Functions/toStartOfInterval.cpp b/src/Functions/toStartOfInterval.cpp
index 0a3a409ea9f..4d716637932 100644
--- a/src/Functions/toStartOfInterval.cpp
+++ b/src/Functions/toStartOfInterval.cpp
@@ -321,6 +321,11 @@ public:
     size_t getNumberOfArguments() const override { return 0; }
     bool isSuitableForShortCircuitArgumentsExecution(const DataTypesWithConstInfo & /*arguments*/) const override { return false; }
 
+    bool useDefaultImplementationForConstants() const override { return true; }
+    ColumnNumbers getArgumentsThatAreAlwaysConstant() const override { return {1, 2, 3}; }
+
+    bool hasInformationAboutMonotonicity() const override { return true; }
+    Monotonicity getMonotonicityForRange(const IDataType &, const Field &, const Field &) const override { return { .is_monotonic = true, .is_always_monotonic = true }; }
 
     DataTypePtr getReturnTypeImpl(const ColumnsWithTypeAndName & arguments) const override
     {
@@ -329,7 +334,7 @@ public:
         {
             const DataTypePtr & type_arg1 = arguments[0].type;
             if (!isDate(type_arg1) && !isDateTime(type_arg1) && !isDateTime64(type_arg1))
-                throw Exception(ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT, "Illegal type {} of argument of function {}. "
+                throw Exception(ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT, "Illegal type {} of 1st argument of function {}. "
                     "Should be a date or a date with time", type_arg1->getName(), getName());
             value_is_date = isDate(type_arg1);
         };
@@ -347,7 +352,7 @@ public:
             const DataTypePtr & type_arg2 = arguments[1].type;
             interval_type = checkAndGetDataType<DataTypeInterval>(type_arg2.get());
             if (!interval_type)
-                throw Exception(ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT, "Illegal type {} of argument of function {}. "
+                throw Exception(ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT, "Illegal type {} of 2nd argument of function {}. "
                     "Should be an interval of time", type_arg2->getName(), getName());
             switch (interval_type->getKind()) // NOLINT(bugprone-switch-missing-default-case)
             {
@@ -371,18 +376,48 @@ public:
             }
         };
 
+        enum class ThirdArgument
+        {
+            IsTimezone,
+            IsOrigin
+        };
+        ThirdArgument third_argument; /// valid only if 3rd argument is given
         auto check_third_argument = [&]
         {
             const DataTypePtr & type_arg3 = arguments[2].type;
-            if (!isString(type_arg3))
-                throw Exception(ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT, "Illegal type {} of argument of function {}. "
-                    "This argument is optional and must be a constant string with timezone name",
+            if (isString(type_arg3))
+            {
+                third_argument = ThirdArgument::IsTimezone;
+                if (value_is_date && result_type == ResultType::Date)
+                    throw Exception(ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT,
+                        "The timezone argument of function {} with interval type {} is allowed only when the 1st argument has the type DateTime or DateTime64",
+                        getName(), interval_type->getKind().toString());
+            }
+            else if (isDateOrDate32OrDateTimeOrDateTime64(type_arg3))
+                third_argument = ThirdArgument::IsOrigin;
+            else
+                throw Exception(ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT, "Illegal type {} of 3rd argument of function {}. "
+                    "This argument is optional and must be a constant String with timezone name or a Date/Date32/DateTime/DateTime64 with a constant origin",
                     type_arg3->getName(), getName());
+
+        };
+
+        auto check_fourth_argument = [&]
+        {
+            if (third_argument != ThirdArgument::IsOrigin) /// sanity check
+                throw Exception(ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT, "Illegal type {} of 3rd argument of function {}. "
+                    "The third argument must a Date/Date32/DateTime/DateTime64 with a constant origin",
+                    arguments[2].type->getName(), getName());
+
+            const DataTypePtr & type_arg4 = arguments[3].type;
+            if (!isString(type_arg4))
+                throw Exception(ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT, "Illegal type {} of 4th argument of function {}. "
+                    "This argument is optional and must be a constant String with timezone name",
+                    type_arg4->getName(), getName());
             if (value_is_date && result_type == ResultType::Date)
                 throw Exception(ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT,
-                    "The timezone argument of function {} with interval type {} is allowed only when the 1st argument "
-                    "has the type DateTime or DateTime64",
-                        getName(), interval_type->getKind().toString());
+                    "The timezone argument of function {} with interval type {} is allowed only when the 1st argument has the type DateTime or DateTime64",
+                    getName(), interval_type->getKind().toString());
         };
 
         if (arguments.size() == 2)
@@ -396,10 +431,17 @@ public:
             check_second_argument();
             check_third_argument();
         }
+        else if (arguments.size() == 4)
+        {
+            check_first_argument();
+            check_second_argument();
+            check_third_argument();
+            check_fourth_argument();
+        }
         else
         {
             throw Exception(ErrorCodes::NUMBER_OF_ARGUMENTS_DOESNT_MATCH,
-                "Number of arguments for function {} doesn't match: passed {}, should be 2 or 3",
+                "Number of arguments for function {} doesn't match: passed {}, should be 2, 3 or 4",
                 getName(), arguments.size());
         }
 
@@ -408,7 +450,10 @@ public:
             case ResultType::Date:
                 return std::make_shared<DataTypeDate>();
             case ResultType::DateTime:
-                return std::make_shared<DataTypeDateTime>(extractTimeZoneNameFromFunctionArguments(arguments, 2, 0, false));
+            {
+                const size_t time_zone_arg_num = (arguments.size() == 2 || (arguments.size() == 3 && third_argument == ThirdArgument::IsTimezone)) ? 2 : 3;
+                return std::make_shared<DataTypeDateTime>(extractTimeZoneNameFromFunctionArguments(arguments, time_zone_arg_num, 0, false));
+            }
             case ResultType::DateTime64:
             {
                 UInt32 scale = 0;
@@ -419,7 +464,8 @@ public:
                 else if (interval_type->getKind() == IntervalKind::Millisecond)
                     scale = 3;
 
-                return std::make_shared<DataTypeDateTime64>(scale, extractTimeZoneNameFromFunctionArguments(arguments, 2, 0, false));
+                const size_t time_zone_arg_num = (arguments.size() == 2 || (arguments.size() == 3 && third_argument == ThirdArgument::IsTimezone)) ? 2 : 3;
+                return std::make_shared<DataTypeDateTime64>(scale, extractTimeZoneNameFromFunctionArguments(arguments, time_zone_arg_num, 0, false));
             }
         }
 
@@ -433,8 +479,16 @@ public:
     {
         const auto & time_column = arguments[0];
         const auto & interval_column = arguments[1];
-        const auto & time_zone = extractTimeZoneFromFunctionArguments(arguments, 2, 0);
-        auto result_column = dispatchForColumns(time_column, interval_column, result_type, time_zone);
+
+        ColumnWithTypeAndName origin_column;
+        const bool has_origin_arg = (arguments.size() == 3 && isDateOrDate32OrDateTimeOrDateTime64(arguments[2].type)) || arguments.size() == 4;
+        if (has_origin_arg)
+            origin_column = arguments[2];
+
+        const size_t time_zone_arg_num = (arguments.size() == 2 || (arguments.size() == 3 && isString(arguments[2].type))) ? 2 : 3;
+        const auto & time_zone = extractTimeZoneFromFunctionArguments(arguments, time_zone_arg_num, 0);
+
+        auto result_column = dispatchForTimeColumn(time_column, interval_column, origin_column, result_type, time_zone);
         return result_column;
     }
 
@@ -449,8 +503,8 @@ public:
     }
 
 private:
-    ColumnPtr dispatchForColumns(
-        const ColumnWithTypeAndName & time_column, const ColumnWithTypeAndName & interval_column, const DataTypePtr & result_type, const DateLUTImpl & time_zone) const
+    ColumnPtr dispatchForTimeColumn(
+        const ColumnWithTypeAndName & time_column, const ColumnWithTypeAndName & interval_column, const ColumnWithTypeAndName & origin_column, const DataTypePtr & result_type, const DateLUTImpl & time_zone) const
     {
         const auto & time_column_type = *time_column.type.get();
         const auto & time_column_col = *time_column.column.get();
@@ -461,25 +515,25 @@ private:
             auto scale = assert_cast<const DataTypeDateTime64 &>(time_column_type).getScale();
 
             if (time_column_vec)
-                return dispatchForIntervalColumn(assert_cast<const DataTypeDateTime64 &>(time_column_type), *time_column_vec, interval_column, result_type, time_zone, scale);
+                return dispatchForIntervalColumn(assert_cast<const DataTypeDateTime64 &>(time_column_type), *time_column_vec, interval_column, origin_column, result_type, time_zone, scale);
         }
         else if (isDateTime(time_column_type))
         {
             const auto * time_column_vec = checkAndGetColumn<ColumnDateTime>(time_column_col);
             if (time_column_vec)
-                return dispatchForIntervalColumn(assert_cast<const DataTypeDateTime &>(time_column_type), *time_column_vec, interval_column, result_type, time_zone);
+                return dispatchForIntervalColumn(assert_cast<const DataTypeDateTime &>(time_column_type), *time_column_vec, interval_column, origin_column, result_type, time_zone);
         }
         else if (isDate(time_column_type))
         {
             const auto * time_column_vec = checkAndGetColumn<ColumnDate>(time_column_col);
             if (time_column_vec)
-                return dispatchForIntervalColumn(assert_cast<const DataTypeDate &>(time_column_type), *time_column_vec, interval_column, result_type, time_zone);
+                return dispatchForIntervalColumn(assert_cast<const DataTypeDate &>(time_column_type), *time_column_vec, interval_column, origin_column, result_type, time_zone);
         }
         else if (isDate32(time_column_type))
         {
             const auto * time_column_vec = checkAndGetColumn<ColumnDate32>(time_column_col);
             if (time_column_vec)
-                return dispatchForIntervalColumn(assert_cast<const DataTypeDate32 &>(time_column_type), *time_column_vec, interval_column, result_type, time_zone);
+                return dispatchForIntervalColumn(assert_cast<const DataTypeDate32 &>(time_column_type), *time_column_vec, interval_column, origin_column, result_type, time_zone);
         }
         throw Exception(ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT, "Illegal column for first argument of function {}. "
             "Must contain dates or dates with time", getName());
@@ -487,7 +541,7 @@ private:
 
     template <typename ColumnType, typename FromDataType>
     ColumnPtr dispatchForIntervalColumn(
-        const FromDataType & from, const ColumnType & time_column, const ColumnWithTypeAndName & interval_column,
+        const TimeDataType & time_data_type, const TimeColumnType & time_column, const ColumnWithTypeAndName & interval_column, const ColumnWithTypeAndName & origin_column,
         const DataTypePtr & result_type, const DateLUTImpl & time_zone, const UInt16 scale = 1) const
     {
         const auto * interval_type = checkAndGetDataType<DataTypeInterval>(interval_column.type.get());
@@ -505,34 +559,34 @@ private:
         switch (interval_type->getKind())
         {
             case IntervalKind::Nanosecond:
-                return execute<FromDataType, DataTypeDateTime64, IntervalKind::Nanosecond>(from, time_column, num_units, result_type, time_zone, scale);
+                return execute<TimeDataType, DataTypeDateTime64, IntervalKind::Nanosecond>(time_data_type, time_column, num_units, origin_column, result_type, time_zone, scale);
             case IntervalKind::Microsecond:
-                return execute<FromDataType, DataTypeDateTime64, IntervalKind::Microsecond>(from, time_column, num_units, result_type, time_zone, scale);
+                return execute<TimeDataType, DataTypeDateTime64, IntervalKind::Microsecond>(time_data_type, time_column, num_units, origin_column, result_type, time_zone, scale);
             case IntervalKind::Millisecond:
-                return execute<FromDataType, DataTypeDateTime64, IntervalKind::Millisecond>(from, time_column, num_units, result_type, time_zone, scale);
+                return execute<TimeDataType, DataTypeDateTime64, IntervalKind::Millisecond>(time_data_type, time_column, num_units, origin_column, result_type, time_zone, scale);
             case IntervalKind::Second:
-                return execute<FromDataType, DataTypeDateTime, IntervalKind::Second>(from, time_column, num_units, result_type, time_zone, scale);
+                return execute<TimeDataType, DataTypeDateTime, IntervalKind::Second>(time_data_type, time_column, num_units, origin_column, result_type, time_zone, scale);
             case IntervalKind::Minute:
-                return execute<FromDataType, DataTypeDateTime, IntervalKind::Minute>(from, time_column, num_units, result_type, time_zone, scale);
+                return execute<TimeDataType, DataTypeDateTime, IntervalKind::Minute>(time_data_type, time_column, num_units, origin_column, result_type, time_zone, scale);
             case IntervalKind::Hour:
-                return execute<FromDataType, DataTypeDateTime, IntervalKind::Hour>(from, time_column, num_units, result_type, time_zone, scale);
+                return execute<TimeDataType, DataTypeDateTime, IntervalKind::Hour>(time_data_type, time_column, num_units, origin_column, result_type, time_zone, scale);
             case IntervalKind::Day:
-                return execute<FromDataType, DataTypeDateTime, IntervalKind::Day>(from, time_column, num_units, result_type, time_zone, scale);
+                return execute<TimeDataType, DataTypeDateTime, IntervalKind::Day>(time_data_type, time_column, num_units, origin_column, result_type, time_zone, scale);
             case IntervalKind::Week:
-                return execute<FromDataType, DataTypeDate, IntervalKind::Week>(from, time_column, num_units, result_type, time_zone, scale);
+                return execute<TimeDataType, DataTypeDate, IntervalKind::Week>(time_data_type, time_column, num_units, origin_column, result_type, time_zone, scale);
             case IntervalKind::Month:
-                return execute<FromDataType, DataTypeDate, IntervalKind::Month>(from, time_column, num_units, result_type, time_zone, scale);
+                return execute<TimeDataType, DataTypeDate, IntervalKind::Month>(time_data_type, time_column, num_units, origin_column, result_type, time_zone, scale);
             case IntervalKind::Quarter:
-                return execute<FromDataType, DataTypeDate, IntervalKind::Quarter>(from, time_column, num_units, result_type, time_zone, scale);
+                return execute<TimeDataType, DataTypeDate, IntervalKind::Quarter>(time_data_type, time_column, num_units, origin_column, result_type, time_zone, scale);
             case IntervalKind::Year:
-                return execute<FromDataType, DataTypeDate, IntervalKind::Year>(from, time_column, num_units, result_type, time_zone, scale);
+                return execute<TimeDataType, DataTypeDate, IntervalKind::Year>(time_data_type, time_column, num_units, origin_column, result_type, time_zone, scale);
         }
 
         std::unreachable();
     }
 
-    template <typename FromDataType, typename ToDataType, IntervalKind::Kind unit, typename ColumnType>
-    ColumnPtr execute(const FromDataType &, const ColumnType & time_column_type, Int64 num_units, const DataTypePtr & result_type, const DateLUTImpl & time_zone, const UInt16 scale) const
+    template <typename TimeDataType, typename ToDataType, IntervalKind::Kind unit, typename ColumnType>
+    ColumnPtr execute(const TimeDataType &, const ColumnType & time_column_type, Int64 num_units, [[maybe_unused]] const ColumnWithTypeAndName & origin_column, const DataTypePtr & result_type, const DateLUTImpl & time_zone, const UInt16 scale) const
     {
         using ToColumnType = typename ToDataType::ColumnType;
         using ToFieldType = typename ToDataType::FieldType;
@@ -547,6 +601,14 @@ private:
 
         Int64 scale_multiplier = DecimalUtils::scaleMultiplier<DateTime64>(scale);
 
+        /// TODO: This part is missing. origin_column is either {} (<-- to check, you could do `origin_column.column == nullptr`) or not {}
+        ///       In the former case, we can execute below existing code.
+        ///       In the latter case, we need to read the actual origin value. As per `getArgumentsThatAreAlwaysConstant()` (see above), we
+        ///       can be sure that origin_column is a `ColumnConst`. The second assumption we can reasonable make is that it has the same
+        ///       type (Date/Date32/DateTime/DateTime64) as the time column (1st argument). Since the method we are in is already
+        ///       templatized on the data type of the time column, we can use `checkAndGetColumnConst<ColumnType>(...)` to cast
+        ///       `origin_column.column` to a const column and then read the (const) value from it, and proceed with the calculations.
+
         for (size_t i = 0; i != size; ++i)
             result_data[i] = static_cast<ToFieldType>(
                 Transform<unit>::execute(time_data[i], num_units, time_zone, scale_multiplier));