There are some possibilities, it all depends on your situation, and what you are looking for rate-wise. Also, are they all either owner-occupied or second homes, or were they used as investment properties. The question is a bit open-ended to figure out. If you have loans on all 3 homes, but can qualify, you can purchase something without selling all of them, as long as you have the right income and assets to cover.
However, I have one thing to say, which some may know the true answer for, although you should definitely consult an attorney. Someone told me that you cannot enter into a contract in NJ if you have something else to sell. I will admit this was from a client who sometimes didn't get everything exactly right, and sounds a little odd to me, but I would check it out anyway.