I would think it is possible to do a task in multiple context. since most handphone have internet function. hence it make sense to add the ability for one take to take multiple context. this also allow flexibility to user own discretion to use this functionality.
It would also be good to be able to run through the context in the main sidebar since usually what take we decide to do for that particular moment is decided upon by what context we are in. For example, if I'm on my phone and have 5 mins, i would like to scroll through the context of phone and see if there is any action within the phone context that can be actionable. hence it make sense to be able to select the context right at the most convenient area, i.e. the sidebars
That's usually a sign that your contexts are to specific. You would need to make a more specific use case that this would address.