Assuming you are asking this question in the context of rental income and expenses, once your property is placed in service as a rental and depreciation has begun, you should not adjust the basis that was originally used.
If you replace something that is considered to be a component of the house (such as the roof), then it will be depreciated on its own starting with the date it was placed in service. The same would be true for your examples of a submersible pump or refrigerator. Those will be depreciated on their own and not added to the basis of the house.
If the assumptions were incorrect, please give some additional context for your question and someone will be able to elaborate more.
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