I am looking to buy a 2 or 3-unit home in NYC. I plan on renting a unit and probably getting a roommate or two in my unit to maximize cash flow early on. So far, the best deal I have been able to find is 5% down with no PMI (80% from Fannie and another 15% from a second lender). The price range for the home would be $1M - $1.8M.

Is there any way I could qualify for 3.5% down instead?

I realize these are already very good terms, but I thought I'd check what is possible. Based on my calculations, even with a low down payment, I can achieve positive cash flow (with aggressive enough house hacking).