Old Chicago schwinn and worksman can both be adapted to take 1 1/8" I've done both. The newer schwinn heavy duti I think takes it also. There are a couple style shd frames, I'm not sure if they all take it.
One thing I like about the Worksman frames, they take 7/8 seatpost. All mine have a piece of 7/8 6061 aluminum solid bar for a seat post. I bought a bunch of cutoffs cheap.