@JeremyECrawford While you've clarified that dealing extra damage (via ability modifier or class feature) with a net is impossible since it has no damage to begin with what about replacing the damage (which is "-") with a monk weapon's damage die as a kensei weapon?

— David Coffron (@dcoffron) December 12, 2017

A kensei weapon can't have the special property. A net has the special property, so it can't be a kensei weapon. #DnD https://t.co/Iiud34trwj

— Jeremy Crawford (@JeremyECrawford) December 12, 2017