No, there is no limit, but improvements made before the rental was available for rent, are added to the basis of the building. Once the rental is available for rent, the improvements can be depreciated separately or even subject for the Section 179 deduction and/or Bonus Depreciation.
If before, add the cost of improvements to the cost of the building. Also be sure to value the land, that amount is never depreciated.
After it is an active rental, expense maintenance fees and list the improvements as additional assets. Each asset then is depreciated by its respective life.
According to the IRS:
"The cost of any additions or improvements made before placing your property into service as a rental that have a useful life of more than 1 year."
IRS Pub 527
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