My old house in Pigtown had a garage that was previously used for parking but a commercial space on the other side of the alley erected metal bars to encompass their parking lot at some point. This effectively narrowed the alley and made the garage useless for parking because the angle wasn't enough for any reasonably sized vehcile to turn into (except for "pregnant roller skate" cars like Fiats, SmartCars or Honda Fits)

So it's probably allowed but you're in for a kafkaesque level of bureaucracy in trying to secure the permits. Ask yourself if it's really worth the headache.