iTunes match and multiple Apple IDs

Due to certain circumstances, my family is left with one computer for the household. This computer is subscribed to iTunes Match. Prior to that, everyone synced thier devices on another mac which is not available anymore. The question is, can they now sync and backup with the computer that is signed in to iTunes Match? If not then is there a way to work around it? Music is not the issue in this situation, it's the backup data, photos and apps.