You *do* *not* *ever* change the basis of an already entered and existing asset under any circumstances. There are no exceptions. Doing so will completely skew the depreciation and depreciation history.
When you have a property improvement that adds to the basis, you enter the improvement as a completely new asset in the assets/depreciation section. Depreciation on the newly entered asset starts on the date it was placed in service. It does not matter when the improvement was paid for, and it does not matter when the work was started or completed. Depreciation begins on the date the improvement is placed in service.
