Notwithstanding an over-zealous strata committee and building management, your biggest problem may come from the local planning authority which will have calculated the number of parking spaces it wanted the block to have when it issued the DA. Be ready for this to be cited in your committee’s objections.
Might be easier just to shrink the cage (assuming it’s lot property) and eventually introduce a car to the space. Or tell the committee you want the space for a mobility scooter. Or tell them you are getting an electric car and this only requires a special sustainability resolution (dubious but worth a try).
Or … sometimes it’s easier to apologise after the matter than ask for permission in advance. Just be sure not a single centimetre of car intrudes over the line and into common property.