The 203 is a great loan for what you are trying to do. There is also a 203 refi product available that I wasn't even aware of. You can't take cash out with it but you can make repairs & improvements. I believe you can use a 203 every two years. I'd talk to a couple of 203k lenders. I can refer you to a national lender for a chat if you wish. How long have you been in the current house? If your credit and equity in the current property is decent, I'd look at getting a lease for a renter on the unit you're living in and refi it or sell it off. Then you could use the 203 to purchase a quad instead of a duplex to accomplish the same purpose of buying a 3rd property. I'm not a lender and others can chime in....there are lenders floating around on the site. You're in a major metropolitan market so there's a way somewhere to get it done...provided the numbers are right and your income & credit are solid.
Beyond that, you can always keep the unit you are in and seek another unit with owner financing....where someone is sick of it or is retiring. Alot of the retiring owners don't mind holding private paper...and it pays them more than cash sitting in the bank at less than 1%.
There are some bright stars in here and some thugs...don't be discouraged. There's nothing wrong with being creative...it will lead to your best returns but, when it comes to federal loan programs...it's strictly by the book. Most of us who have been around long enough have seen plenty go to jail for mortgage fraud so that is the concern raised by others. Luck!!