Yes you can. We are doing that now. Buying an existing home for $420 and adding the cost of a new pool build of 46K. The bank will appraise the house with the pool. Lender says it depends what neighborhood. If it's a neighborhood where a pool is considered an added amenity, in our case it is. People pay a bit more for a house with a pool. Sometimes pool doesn't appraise as a dollar to dollar value so you'll have to come up with the off set. For example, if the pool appraises at 50 cents to a dollar, and if the cost of the pool is 46K, then you will have to find 23K to cover the difference at closing. Thankfully, most have appraised at dollar to dollar lately. I guess it also has a lot to do with the market and in Houston, it is hot hot hot right now.