Why Can't Teams play in the MLS & CPL Simultaneously?

Think about it. Teams around the world play in multiple competitions simultaneously. Toronto FC might play in the MLS, CONCACAF Champions League & Canadian Championship in a given year (2 for sure) for example. Why not just have Toronto, Vancouver and Montreal just play in the CPL and MLS? I'm sure they could have players signed specifically for CPL and some for MLS rosters. They could then loan back and forth like some teams do with their USL B squads. In this case though, they would be the "same team." It might raise the profile of the CPL having those established teams in it and allow for some really exciting players to be involved in the big games. Thoughts?