Just get a conventional loan at 97%, it's a Fannie Mae product.  

@Jed Devine. 10 is the limit of financed properties you can have through Freddie Mae, unless you have 10 investment properties and are purchasing a primary residence, then you can add the primary residence.

There are wide divides in the multifamily industry and depending on the loan amount there are different lenders (or lender products that you are looking for):Loans under $1M - local banks$1-5MM - Small balance Freddie$2-20MM - FHA (if you are looking for a longer term/fully amortizing debt)$5-50MM - Fannie Mae/Freddie Mac$10MM+ - Portfolio Lenders (large banks or insurance companies). 

seems to state that a blanket loan wouldn't work, because Fannie Mae counts the total number of properties you have financed, not the number of loans themselves (and it doesn't matter if the loans are sold to Fannie Mae or not):These limitations apply to the total number of properties financed, not to the number of mortgages on the property or the number of mortgages sold to Fannie Mae. 

Once I got it renovated and rented I got it refinanced through a traditional fannie mae refinance mortgage 75% LTV 30 year am 5.125% interest rate fixed.

I also downloaded a Fannie Mae Form Uniform Residential Loan Application, and it looks pro, but I haven't read through all the fine print yet to see if permission to pull credit, etc, is included.I found a tenant screening service here on BP, RentPrep, and I would think that it would be the same information I need, but not sure if it will work legally to use as a loan application screening instead of a rental screening. 

I am interested in buying multiple SFH properties and like to use Fannie Mae/Conventional loans as much as possible due to their great rates. 

Fannie Mae published new guidelines for lenders on November 8, 2017 that allow transfers to LLCs!

@Jim ButterfieldFannie Mae Freddie Mac reduced the number of investment loans they're buying, so that has a factor on investment loan costs.

For example Fannie Mae multi-family loans require a GFI in kitchens & baths.