As mentioned, your only conforming residential loan option is an "investment" conventional loan since you are not occupying the unit.Your only other options would be to get more creative with a "commercial loan" which is effectively much less regulated. 

It appears that the 3 unit property would at best be legal non-conforming depending on the year that it was converted to 3 units.Perhaps @Dorothy Ma is aware of the situation you are considering and can comment in more detail.

Are the terms/requirements/guidelines for a conventional/conforming Rate and Term refinance different than a cash-out refi? 

I was trying to get jumbo loan down to a conforming with equity.

I can get a $10m commercial loan easier than I can refinance on of my $100k SFH (I still have many of the homes I bought when I was getting started)At some point you just shrug it off and realize that our conforming loan rules are dumb and designed only for W2 people and just move on.  

The Mortgage Professor has a table for conforming wholesale rates:Mortgage Professor

My tax returns are still such that I can finance a $10m apartment complex easily, but can't refinance my own $1m home.So there is no way I'm going to try to grow a real estate empire by dealing with 1-4 family pinhead lenders (or rather pinhead originators that have to fit you in a conforming loan box)Also, my goal was always to have 1000 units (which seemed huge at the time, I have 1500 units now). 

Thus, you're left with either qualifying without that income, or going with a non-conforming loan.  

Also FHA is really 1.5% more if you factor in the other fees so it's more like 5% even though technically it's 3.5%; there are some credit unions that give awesome 5% down conforming loans without those fees. 

@Peter Welch check to see if the property is zoned to be "legal non conforming".