It would be pretty easy for a fleet service to also provide a bin that you can persistently store your stuff in. When you summon a car, the system puts your bin in before it goes to get you.
I envisage systems of standardised storage lockers, you can pull the whole locker into your car, 4 fit in the car for 4 users, you can wheel them into work, or lock into cabinets around the place, when there's no car parks they'll be lots of free space, 1% can be for storage lockers.