I own a Pilates studio and have seen several clients who also see one of my other instructors. I actually like it a lot. Everyone has a slightly different style and sometimes the way my other instructors do things resonate better with the clients than what I do and vice versa. It’s also nice to have more than one set of eyes on a body to figure out what will best meet their needs. That said if I wouldn’t feel comfortable with them training my clients I would never have hired them so I have a high level of control. In the past I have taught a class once where I taught the tues night class and another instructor who was terribly unqualified taught the same class on Thurs. night and it was a disaster for me. So how about a qualified yes if the other trainer is compatible with you and your style. I also have some clients who do Pilates with me and see a traditional personal trainer and that has worked well as well.
They do it in Physical Therapy settings, although it is probably not quite as split. For example, if one PT is out, another PT will see that patient.
I think it could work, but why not just schedule them specifically on days where you can train them twice per week on your own? You would have to find someone that was really on the same page as you. Anyone too ambitious will try to take the clients from you. Likewise, your client might develop a preference for the other trainer over you, or vice versa. I would avoid it unless it was the only option.
I guess anything can work if you’re clear about expectations and the clients goals.
I would make sure everything is written down and the trainers discuss programming on an ongoing basis
Ultimately the client has to be 100% on board with it and has to succeed with this model.
Personally, this is not something I would do, I think it would be too conflicting.