rebuilding/frankenbike query
Unequivocally, yes, you can - it's just a matter of whether or not it's worth it to you.

Without seeing pictures or details: to avoid unnecessary added expense, you'll want to stick with frames that have:


The same head tube diameter, so you don't have to replace the headset
The same bottom bracket shell width (usually 68mm or 73mm), so you don't have to replace it and/or the crankset
The same rear brake mounts, so you don't have to replace that too (V-Brake/Braze-ons lower than the rim, U-Brake/Braze-ons higher than the rim, or cantilever/a hole in the center, disk brakes/two holes on the non-drive side near the hub). However, I'd probably go with V-Brake mounts and replace the rear brake if it has anything but disk.
The same seat tube diameter, so you can re-use the seatpost and clamp