Hey Angie,
So if your current home is a FHA that you are going to Refinance to a conventional then you will need 25% equity to make the switch or cash to close to bring the loan to to 75% Loan to Value. @Wayne Brooks had it right, you will have to explain to any lender that you are making the switch and intend to live in the new multifamily and supply a reason for the move.
Another option for a second home that you have is a Freddie Mac Home Possible. If you have lived in your FHA for a year and don't quite have the 25% equity this will be a great option for you as you can leave the FHA loan alone until you have the 25% equity and still move into a new property. Instead of the the 3.5% down for FHA the Home Possible is as low as 5% depending on credit which still offers a great option for affordability. Unlike the FHA loan which has Mortgage insurance for the life of the loan the Home possible follows conventional guidelines which mortgage insurance can be cancelled at 80% LTV. This loan like FHA requires owner occupied for minimum of a year. The downside of this loan is that it is only available if you have ownership in 2 mortgages or less including the Home Possible.
Best of Luck!