@EvanMetag
Yeah, pretty much the only way to do this is as @adam deltinger said to have a common Team among them and have channels for each department that can be @channel mentioned. The downside to this, is it's open to everyone in the Team, so yo would see these conversations, assuming security isn't an issue this may work fine, but if things are confidential in any way it makes it a big more complicated.
Ideally Shared channels like Slack has would work best in this scenario and one I hope Microsoft can get implemented some day. Where you can have a common channel shared between two teams, which would bridge this gap.
Another feature coming to Teams in the near future and I hope we see more of it at Ignite is Targeted Messages. You could utilize this feature to basically create groups of people and use @groupofpeople to mention those individuals, so you could define who is in what department, office, field workers, cashiers etc. and then utilize those groupings to target communications.
Sometimes e-mail (ugh I know) still works in certain scenarios better for the time being as well. I'm sure some dev's could create Apps to handle Shared channel scenario and surprised no one has created one yet since I've seen some apps that sync Slack and Teams messages between two Teams. This same thing could be utilized (probably minus threading).
Anyway, my 2 cents :)
