From what it sounds like, you found a home that is owned by a bank or mortgage company, the bank or mortgage company said that it had to pre-approve you for a mortgage before they would entertain your offer, they approved you for a loan in a certain amount and that now you find another home you like more.
If I understand your question correctly, you want to know if you can get a loan from the same bank or mortgage company to buy a different home that might not be theirs. The answer to your question is more than likely a great big “yes.” There are a few catches, though.
Many mortgage companies and banks offer more favorable interest rates to people buying homes that the bank owns through foreclosure than it does to the general public. If you buy a home from someone else, the below-market interest rate that they would have offered for financing the purchase of one of their homes probably won’t be available if you buy a different one.
Also, you will need to submit some new paperwork — alot less than the first time around though — and the underwriter will have to re-examine your application. Assuming that the mortgage payment, taxes and homeowner’s insurance aren’t too much more than for the house you were originally interested in, there probably is very little reason to worry about not getting approved. So, even though the mortgage company won’t have you as a buyer for one of their homes, I’m sure that they will be more than pleased to have a relationship with them as a borrower. I hope it works out well for you.