It all depends on how much your 1st 2 homes are worth. If you owe 275k on 600k valued homes, then yes. However, if you owe 275k on properties worth 300k, then the answer would be more towards no. Another factor is how long you have owned the other rental property and what your rental history looks like. I would suggest contacting a local mortgage broker and explaining your situation over the phone. He/she will quickly be able to point you in the right direction.Good luck!
My suggestion would be to buy a distressed property(foreclosure/short sale) and live in it until you can find employment; then sell it for a profit and move on to the home you actually want.Cash is king when buying these properties, and there are a number available that are "no-brainers". As an owner occupant you would be able to scoop up the home run deals before investors are even able to make an offer. Fannie Mae, Freddie Mac, and HUD allow owner occupants a minimum 10-15 days to view and offer on their properties before they open the floodgates to the general public.This is what I would do if I was in your position; however I already own a home, so I would be considered an investor.Knoxville is great, you will love it here.