2-4 Unit Multifamily Acquisition in New York City

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Looking for anyone who's brain I can pick about their relevant experience investing in small multifamily in NYC  or other high-cost entry markets around the US-

I work in commercial and am interested in making an investment in one of the outer boroughs of NYC. I can model a deal no problem and tell when the numbers make sense, but I need some suggestions as to how people navigate financing in low cap rate environments where even crappy MF properties are going to run at least 350-400K per unit. I have around 100K cash and dont plan to invest until the next market correction, and will probably have about $150 by the time that rolls around. Still, a down payment on a modest 3-4 unit is going to be around 400K if I were to put down 30-40%. FHA regs are pretty confusing to me and I think that even if I were to occupy, the loan wouldn't be for nearly enough considering their maximums.

Does anyone have suggestions as to how to navigate debt in a situation like this?