Just to clarify, are you wanting to add a 3-car garage, or do you want to add an additional spot to an already existing 2-car garage?

I ask because 12'x20' seems awful small for 3 lawnmowers, much less 3 cars.

Do you have an HOA that would have to approve? Look at your survey to make sure there are no required easements or setbacks.

I thought about doing this with our house but had a bunch of hurdles to jump and decided to just say screw it and built a shed in the back instead.

We added a third garage bay (10' x23') to our existing two-car garage back in 2008. We only had siding and a tiny amount of brick to match, so it wasn't too expensive/hard. We got four bids (two were close to $15K, one was $24K, and one was over $30K). After reviewing previous jobs of the contractors and talking to others around town, we decided to go with one of the $15K contracts. No regrets, no problems. The electrical panel was already in the garage (had a few empty spots for new breakers), so that helped keep the cost down. However, we did have to relocate the AC compressor.

We had an asphalt driveway which was not in great shape, so we did spend an extra $5k to replace the entire driveway, as opposed to just adding as new section. So, the total cost was really $20K.

Obviously, these prices are nowhere near today's cost.

We did remodel the interior of the entire garage in 2018 to add a bunch of 220V outlets for woodworking equipment, metal cabinets, and a garage heater (so I could work in it year round, as it can get cold in Maryland). Sold the house 11 months ago for an insane amount.