Refi issues when adding an ADU to a duplex in CA?!?!?

[Oscar Miguel]

Hello everyone, uber noob here...  Thanks for all your insight and support!

I purchased my primary residence, a two-building duplex close to the beach in San Diego. It's been a great buy so far, bought it from a flipper for a very good price and the existing tenant is military and a great person. I began the permit process to add an ADU to the building with the current tenant. The numbers will be great after this and my goal was to refinance out of FHA after I'm finished with construction and the ADU is rented. Then use FHA to go find another duplex or SFR that has room for an ADU to be added.

I spoke with my mortgage broker today to let him know my plan. I'm still about 3-4 months from the completion of this project but wanted to share this plan with him and get whatever ground level plan going. He told me that if I add the ADU to my duplex, that it will be next to impossible to find financing. That for my plan to work, I will need to go through a different permitting process so that my property becomes a "Triplex"

My questions for everyone here is:  Is this correct?  What options do I have?  Any recommendations?

There is a vast wealth of knowledge on these forums and many of us learn from the questions others ask.  I hope all is well with everyone, stay safe and thank you for your input!!!