I've seen this done quite successfully. Each player had a stable of PCs (or rather, was allowed to have a stable of PCs). An adventure would advance time - but for that specific sub-group. So perhaps Amberle, Brandar, and Chrothgar wouldn't be available until "Day 34".
These always had both big overplots going on plus the adventures the individual groups were pursuing at the moment.
Logisitically, usually several adventures were in-play at once depending on who showed, though the easier version of that would be to (a) try to be more episodic and (b) allow characters to join mid-adventure as long as they were free. It's hard to be episodic at all times when you have real plots and not just hex/dungeon crawls.
The one I was in was "The Adventuring Company Company" - basically a bunch of adventurers who did well, and sponsored newbies to go do all the other stuff they didn't have time for. And pass down their outgrown magic items. In an FR setting where an Adventuring Charter was really expensive, so it was a great deal, and people became senior members quick enough.
One from a blogger I read is a mercenary-company-type of setup but with adventurers, and has advancement within the ranks with perks and responsibilities.