@Ruben E Sanchez
I'd like to share an experience I had with a property similar to what you're aiming to make. It may or may not apply to you and may or may not be an issue in your area. Last year I was trying to buy a property that had a single family home with a duplex on the lot. The big hurdle was how it would be appraised and treated by the bank. The most economical way was going for me to finance it as my primary so I could live in one unit and rent remainder, then move out once terms of occupancy had been met so I could rent all units. Since the duplex was on the same lot it wasn't going to be appraised as a duplex, rather as an addition of some sorts like a pool house. That was preventing it appraising to the price they were asking. The alternative was to go commercial which of course required much more money down. (15% for that lender).
I don't know if I explained it clearly but basically, having the house and multifamily on the same lot made it more complicated and somewhat interfered with the potential of each. Here's why: Comparable single family houses in that same neighborhood were already selling for 250k plus WITHOUT a duplex on the lot. This property was for sell for less than 250k. Somebody ended up buying it with hard money.
If you're planning on staying there forever, perhaps it's a non issue for you and the duplex you want to build will just help you live for cheap/free plus earn some income.
Did you say your addition is unpermitted? I'd be concerned it gets noticed by an inspector when constructing the new property? My understanding is they can find out about unpermitted additions and make you take them down.
Can your lot be split so the new duplex is on a lot of its own? would it be accessible without crossing the main house property (if not than maybe an easement if the lot can be split)