I believe that switching and sharing context are skills that can be learnt and exercised to be improved.
With that said, we might want to learn more about the underlying rules and modifierss to those activities. The depth of the context itself, for example, is a huge modifier on how easy would result switching context, but not necessarily to share it. One clear modifier for both is the amont of attention we need to dedicate to a task. We can share a task that require our full attention, but then non of the participants would, or should, be able to attend any other task.
Thinking mainly about how I managed this context switching along different environments and internal states, I came with an idea that I believe would help analyze and boost both skills.