This is exactly what we do at Missive. We are a collaborative app that merges email, chat and tasks. Every conversation is scoped and displayed like email threads: with a list of participants, subject and summary. This way nothing gets buried under generic categories. This design forces you to organize all your communication (external and internal) as well as todos in a much saner way.
I wrote about it a while back:
What started out as a collaborative email client may turn out to be more than we expected…medium.com
Would love to know your thoughts!