It is my understanding that simply replacing certain items is not considered a capital improvement that would affect the basis. However, suppose the replacement is an overall better product such as a more efficient and powerful submersible pump or an energy saver refrigerator with more features. In this instance, could the “improved” item adjust the basis? This is assuming it is not installed as a repair which I don't believe can be included in basis.
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.
If you're trying to calculate the capital gain on the sale of your home, an unofficial rule of thumb is that if you can carry the improvement out of the house, it's not a capital improvement to the property. Thus a new refrigerator or microwave would not qualify; new kitchen cabinets would qualify.
This IRS Publication lists some common capital improvements (Scroll down to "Basis Adjustments"):
https://www.irs.gov/publications/p523