There are 5 surfaces for each tooth, but you could have many small fillings

Usually four or six.

Your Question is slightly vague in that it does not specify a time factor. I am going to presume you mean " how many fillings can a tooth have at one time". There are five distinct surfaces on a tooth that can have fillings. so theoretically you could have five individual fillings on one tooth. Most of the time teeth are touching so two of those surfaces require access from a different surface to fill that surface. This leaves you with possibility of four different fillings on one tooth most of the time.

Teeth have upwards of five surfaces on each tooth. You can get a cavity on any or all of the surfaces at the same or different times.

I suppose you can have a few filling on the same tooth but at some point the tooth that has a large filling(s) it will get weak and fracture prone.