As Brad said, I think that even when you have your own horse, it is important to ride another horse every once in a while. But other than that, I wouldn't want to be the owner of more than one horse. It is already a lot of responsibility to have one.
Personally ever since I started riding more than one horse, my riding has improved a lot and I love having to constantly keep thinking about how I need to ride the two horses differently. Riding more than one horse helps a rider to have a more adaptable seat and riding style.