Multi-Family Home w/ Livable Basement unit?

[Tim Lee]

I am currently looking to house-hack a 4-plex, maybe a 3-plex if it cashflows well enough. I just want the house to be able to break even while I am taking up a unit, and then leave after the FHA-required 1 year to let the house cashflow normally. However, finding a unit like this is obviously hard, and I've heard others' suggestions about living in a sort of unofficial basement unit as to not take up one of the legally lease-able units.

I am wondering if anyone had any experience searching for these kinds of properties. Is there a keyword people use, or do you really just have to ask the agent/seller if the property has such a unit?

I am also wondering how much it would cost to take an existing basement and convert it into a livable space, either as an off-hand unit for me to live in, or as a fully legal lease-able unit. I am sure the cost to make the space just livable vs actually lease-able is quite different, so I'd love to hear if anyone has a ballpark number for either! I definitely don't want to dig a whole new basement, though, since that is way too expensive for my budget.

Anything helps! Thanks in advance