More than one person in my house is interested in the secrets and puzzles of Fez. However, even though it has a save feature, I don't see how I can switch between saves (thus allowing multiple players to start and stop at different points). If I try and choose "Start new game" it says it will delete all progress. Is it possible for two people to play Fez on the same XBox with different save games?
Not with the same profile on the same hard drive. You can use separate memory cards, storing one save game on each (you're prompted at startup). Likewise, every gamertag can have its own save on your hard drive. I'd recommend just using different gamertags for each player.