What does 'what we've got going on' mean here?
We are run by the best owner/chairman/management team I've ever known. Everything they've done has pretty much been done right. If they decide its in the best interests of the club to bring him back into the fold, I trust that decision...because none of us truly know what the reasons are...but they're not going to want to ruin what we've got going on.

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In this case it refers to the management. "What we've got going on" means "the situation (the way the team is being managed so well) as it is now". This is basically a casual, informal way of saying "the status quo".

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"What we've got going on" = "what we are doing at this moment" = "our current situation".  The suggestion is that the current situation is actually quite good and positive.