It already has happened, except it was called Leverage. That show basically was a modern Mission: Impossible. Sure, it was about a team of Robin Hood-style con artists rather than spies, but the fact is that M:I was always basically a heist/caper show at heart; the spy thing was just because '60s network censors wouldn't have approved of a show where the heroes were criminals, so they needed a patriotic justification for their dirty tricks and con games.
Yeah I tried watching a few episodes of Leverage, but it was just a little too cutesy and lightweight for my taste.
Then you probably shouldn't touch Hustle either. It's very similar, but at times the main characters can come off as even more unbearably smug.
Burn Notice started out as a sort of Mission: Impossible meets the A-Team. Even once the actual 'Burn Notice' plot played out, the 'victim of the week' plots tended to alternate between small time and big time 'missions'. So one week they could just be protecting somone from an abusive ex, the next they could be trying to catch a genocidal ex-dictator. The only real problem is that (like most shows of its type) it had a formula that can get pretty repetitive.
Theres always the first season of Danger 5 and movies like Kingsmen if you want an absolutely bonkers pastiche. I'm kind of curious how The Man from UNCLE is going to play out. It looks like it's going to play the whole thing fairly straight, albeit Illya looks like he's taken a few levels in grouchiness.