Selected Answer
Since your question is whether it is possible, the answer is "yes". If your question is then extended to whether I can help you, my answer would be "probably".
First, please explain the logic. What is the point in having an end date if the end date is moved without user action? Would full automation not destroy the purpose of the sheet's information? Perhaps you like an extra column, like, "original end date" and "rolled-over end date".
Second, logically every end date must be calculated from a start date. If you want the old end date to be the new start date the task requires VBA. The change wouldn't be fully automatic like a formula. The change would be made every time you open the worksheet. That is probably good enough for your requirement. Therefore the big issue is whether you want VBA or not. If you want a formula-based solution you need to have a start date that never changes (meaning an extra column in your worksheet). The end date would always be calculated based on that date.
Third, both formulas and and VBA need precise rules how the end date is calculated from the start date (even if the old end date is the current start date). Your formula in F3 gives a hint but hints aren't suitable substitutes for precisely expressed rules.
