Ability to change Team inbox members through REST API

In bigger organisations, we need to schedule agents to work on different topics throughout the day by using a schedule. This schedule would dictate that Agent X would work on Billing for the first 2 hours, then on L1 tickets for 3 hours and so on. Right now the only way to work on Billing is to be part of the Team inbox Billing. Same for L1. But if an agent is part of those 2, we cannot prioritise how they are working on those easily. If we had the ability to change teammates from one team to another dynamically though API, it would make things much easier.