The foundation
Los Angeles houses sit on three common kinds of foundation. A raised foundation with cripple walls and a crawl space, common in older houses. A slab on grade, common in post-war tracts. Piers or caissons on a hillside, sometimes mixed with the other two after decades of additions. The drawings on file may say one thing; the house says another.
I expose the foundation where it matters to confirm its type, depth, reinforcement and condition. A new floor needs footings sized for the new load, and the usual answer on an older house is new footings doweled into the old ones, or grade beams that pick up the new posts.