That would indeed be very nice to have, but I am not aware of any way to accomplish that directly with MusicBee.
What you might try (but it's a lot of work and not for the faint of heart) is try accomplish something like this through Logitech Media Server.
Logitech has their Squeezebox (hardware) players which can be easily synced to each other over a network.
When you don't have their hardware, you can install software Squeezbox players instead (called softsqueeze if I am not mistaken)
You should be able to get them playing synchronous over a network as a standard feature, using Logitech Media Server as the library.
The part where MusicBee could still play a (minor) role in such a setup would be if you would configure your local softsqueeze player as a tool in MusicBee, then you could send any track in MusicBee to the softsqueeze player(s).
I can't vouch for 100% this would work, since I am using hardware Squeezeboxes myself, but it might be worth a try.
edit,
A quick google search found that this might work better with 'SqueezePlay' instead of 'Softsqueeze', but you'll have to do some googling yourself before you decide to go this road.
edit2:
Just tried this out for fun myself. It is working. But for now I can't get MusicBee playing a role in this setup.
I can't get LMS getting to play from within MusicBee.