I think you could fit some kind of basket on the front, like a cycle basket, but it would block your headlight so could only be used daytime and you prob would need to remove it at night. I always ride with my light on for safety, day an night, so I would prefer to leave it clear.
You could look at panniers? They fit on the side. Not sure of any specific for scooters tho. Or you could ride with the backrest/pillion seat up and attatch a large plastic box from a diy store on it when going shopping. May not look too pretty but it would work and you can take it off once you get home.