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.