In short, I want to assign up to 10 horses or ponies to this rider, of which do not exceed the rider's level. All the horses are prepared to train in all disciplines, I think. Is there any other reason that I cannot assign more than the intial three ponies to her? I prefer to pay one trainer than two, especially if it is unnecessary.

The horses and riders MUST be on the same level in order to be assigned.

Thank-you Jello Warmbloods. I didn't realize before that the rider must be exactly the same level as the horse's highest level.

Sometimes the levels aren't exactly the same, though. You can have a horse showing in D3, CC2, J2 that might have a level 4 rider. It can happen if the rider levels up AFTER you assign him/her to the horse. So you assign a level 3 rider when the horse goes to D3 and before the horse goes up to D4 and needs a new rider, the rider goes up to level 4. That rider can stay on the horse, but if you remove him from the horse, you can't reassign him to the horse until it is level 4. I'm sure that's clear as mud.