As [@MelonHead] said, this is something we used to (and still somewhat) do on Gaia. We treat Gaia as a multiverse (referred to as the "Gaia Mainstream") where characters from any given setting can pop up. We have people who run events -- whether fighting tournaments or DMed mini-campaigns -- and these events are very condensed in terms of time, usually. Less so for tournaments, but even then we try to use a very clear timeframe for our events, and I think this aids a lot in promoting activity.

For example, a long-since-departed player named opaj used to run events; he basically developed the idea for those of us on Gaia who play in the Mainstream and he coined the term Gaia Mainstream. His method was something like this: Develop a campaign or event and tap a few people to DM it with him. They would then DM according to a specific schedule, and during those scheduled times people were meant to post as much as possible, within reason.

So, for instance, during one event he might say "The DM team will be rolling the story forward Thursday through Sunday. We will NOT DM NPCs or advance the plot on Mon-Wed. This event will last two weeks, and will conclude on the second Sunday." Basically, he would use specific timeframes to encourage people to post by saying "here's our active period, post then to be part of the plot's advancement" while having off-days where it would be less DMing and more general roleplaying to grease the wheels of the story. During this period, they might still DM casually, but more for interaction than for pushing the story to its conclusion.

All of opaj's events were ran on very particular, very condensed timeframes. I can't remember his events ever being longer than two weeks, and I think he ran one in a single weekend of constant posting. Admittedly, this is back when most of us were in high school or college, so we had more time, but I think the approach still has a lot of merit because a) as adults, we have some control over our schedules and b) it gives us an impetus to roleplay because we know we're working within a very specific timeframe, instead of a more lackadaisacal "it'll finish when it finishes" approach.

opaj-style events have fallen by the wayside on Gaia at the moment, but as someone who participated in one, I can tell you: they were immensely enjoyable, especially because you had this atmosphere of frenetic activity where everyone was just rolling along at a good, steady clip of roleplaying. No waiting for days or weeks, no hemming and hawing. Just people jumping in and playing and getting shit done.