Why, If I understand correctly arenas work kind of like that... The problem is in combining mission objectives of both teams, handling possibility of mission failure where previousle weren't any and other devilish details... But... But there are Safeguard/Mayhem missions! it's guaranteed that both teams would have matching objectives, there's already possibility of failure on both sides.
Then there's a human factor... Randomly deciding whether it would be PvP or PvE safeguard simply would annoy everybody, letting them by mutual agreement only would turn them in yet another PvP, mode, Uba-700N required. And forcing PvP won't work, as low-level toons lose their precious jetpacks. 
Just random thoughts here....
I'm quite new to the boards so maybe this has been suggested a hundred times and perhaps from a technical point theres a million reasons why it cant be done....but the zombie invasion and Jade Warrior's Epic Battle post got me thinking...
THE CROSSOVER EVENT
A new character (similar to the Gamesmaster or the Watcher) weakens the barriers between Paragon City and the Rogue Isles.
Event Mechanic:
Teams entering mission doors could face a team of (player) villains instead of the usual mobs, npc's etc. This would be a random event based on teams from either side being roughly the same lvl and starting missions in a similar-ish timescale, however this selection process would be hidden from players so the element of surprise is there. If this is too difficult, then perhaps selectable missions at train stations could work, with special mission zones.
Special rewards would be offered during the event in PvP zones and the Arena. Instead of GMs why not have some AVs spawning?
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