I did a partial lease on a horse which meant I paid to ride this horse 2 times a week. I had my days, and my days the horse was completely in my care. My portion of the money went to help the owner pay the bills such as boarding, farrier, and veterinary.
The problem I found with this situation was people had several different riding styles. Even if we all did the H/J, I would work on lead changes one day and make great progress, but the next person to ride would completely undo what I had done and caused even more damage in something else. This is why I backed out of this type of situation.
In my opinion, it wasn't fair for the horse to have so many communication differences. I'm sure she was just as confused as we were. Certain horses may be able to do this just fine and not have problems with different people riding every week, but this particular mare was quite sensitive.
Yes from what I understand it is similar to a partial lease. And I agree with Heather I think the horse would get quite confused causing all sorts of problems. But maybe there is a way to minimize this by screening the riders better. I have too many horses and not enough riders and the riders I do have live in apartments or urban areas where they can't own a horse. I'm thinking that if a horse would be competing at all then the rider would need to go with a full lease not a partial. Thank you all for your replies they are very helpful.