Since your subject is a 2 unit, then the third unit in the back makes it a three unit. Whether or not a 3 unit is legal per zoning for your subject IDK, assuming it is, or the lender accepts a property with an illegal use, (which you would disclose ) Indeed, MLS often does not disclose permits, but in my area, we can do an online permit search with the local building division. If the third unit shows up on public records as sf or descprition it is usually permitted, and of course, one can contact a RE agent and ask.
Though we can not outright trust AI, its pretty good. Below is its answer when I asked will fannie finance a duplex with an ADU-
AI overview - No, a duplex cannot have an accessory dwelling unit (ADU) for Fannie Mae financing, because Fannie Mae does not permit ADUs on properties with two or more dwelling units. An ADU is only allowed on a primary single-family home (one-unit property), and the property must have only one owner.
- Fannie Mae definition: A property with an ADU is defined as a one-unit property with an accessory unit, not a multi-unit property.
- Ineligibility: Properties with 2 to 4 units, such as a duplex, are not eligible for an ADU under current Fannie Mae guidelines.
- Requirement: The property must be a single-family home with a single owner, and it can have only one ADU.