Help with next FHA or VA loan

[Richard Pina]

Good morning, I'm starting my Journey and may have ran into an issue. I purchased my first single family in 2019 with an FHA loan and i am ready to purchase my first multi family. I am currently working with the bank and was told at underwriting they cannot give me another FHA loan do to me currently having an FHA loan (i was under the impression after 1 year i am eligible to move and since i am going up from single to multi family it was fine). Now i am wondering if i was to use my VA loan to purchase the multi family property would i run into the same issue. My plan was to use the FHA or VA loan in my current market then some time after (hopefully 3-6 months) purchase a property either out of state or in my state in a cheaper market with a conventional loan or even find a property to brrr as i have a good amount of on hand cash and plenty equity in my current home if needed. Any help will be graciously received.

Thank you