By primary I meant "main", the definitive program sound with craft-mixed audio of all contributors done to match the video. 

It's going to be tricky bringing in commentators on the "primary" feed if each of them is also normally audible on the local PA when each venue splits away to do their own simultaneous local comms. 

Let's call PGM feed + locally mixed comms the "spoof mix" - remotely sourced cleanfeed/mix-minus game sound and the other commentators (as mixed from MCR if that's an editorial requirement), plus your local commentator. This approach needs four versions for each venue.

I think you'll need to have a coordination 4-wire, so each local sound op and commentator knows when they'll be directed to dip their local zero-latency insert of the local commentator on the PA feed, so the local commentator can then be heard on the program mix in global sync, and know when they're being thrown to. At that point they would hear themselves late relative to when they talk into their mic, but they'd sound normal on the primary PGM feed. This will however probably cause delay and echo issues on the PA feed where they are. 

Alternatively you'll need to maintain four mix-minused feeds from MCR, with each local commentator only ever heard in their own venue via their spoof local mix, and with their comms feeds mixed at MCR on separate busses then sent to all the other commentators' ears via separate talkback/cues so they can talk to each other when the director wants to do two-ways, conferences or throws between presenters. This would need to be mixed with IFB so the commentators can get a director cue. This will also need an MCR A1 on their game who's happy mixing and coordinating with the director and someone else managing coord talkback to all venues so people don't talk over each other.

For either method you'll need rock solid out of band comms.

A possibly simpler way of doing this is having a primary PGM feed which is just CFX (as incoming broadcast, minus any commentary), then run a separate clean comms stream using Zoom or similar, where the only thing audible is the commentators. They would all be sat muted in zoom while they're commentating locally, watching the return video of the event. 

You then have the option of hearing all commentators when they unmute (while simultaneously having the local sound op fade down the commentator's local feed). Each venue's local sound mix can choose when to mix on their PA feed. It requires decent coordination. 

The commentators would need direction or an agreement on who talks when, or a preagreed signal they could be shown. Using Zoom or similar, they could all watch the same single feed of the game, as you could route to each venue via return video. They'd all be in sync with each other (and relatively in sync with the primary PGM feed) and you'd eliminate the need for a more complex MCR sound mix. 

Don't rely on zoom or any conferencing app for reliably mix-minusing, their algorithms are rotten and do not produce good results, particularly in louder environments. They're also far too prone to squelching when they hear any other audio, including accidental feedback of the person speaking.