The ceilings in this place proved to be an enormous pain and a significant lesson. My first instinct was to preserve them if at all possible.
Upstairs, this made sense, because the attic was filled with 18 inches of blown-in cellulose insulation. The ceilings appeared to be mostly old sheetrock topped by strapping and then a layer of stapled up acoustic tile. We would not only have to deal with the tile and sheetrock, but also the cellulose.
But the tiles were in bad shape. So we screwed strapping against the the old acoustic tile in preparation for sheetrock.
Downstairs, however, was a different story. The ceilings were in better shape and I figured I should save them. But we had wiring to do, so that meant spending hours snaking wires. And in the process, the ceilings became damaged enough that they eventually were all ripped down. We would have been better off demolishing them in the first place.