You can line up several missions at a time - just so long as none of them are left long enough to get sent back to the Unclaimed Badfic list. To avoid this, try working on as many as you can at the same time. (For instance, if you have missions lined up for more than one agent pair/trio, you might be able to do a mission for each group, simultaneously.)

Additionally, don't take too many missions. Don't completely wipe out the Unclaimed Badfic page, and don't take more than you can handle.

Like me: I've claimed two or three fics at the moment to spork, because I can handle them and I know the missions will be finished by New Year's. I'm also making myself wait until those are done before taking any more, because I don't want to overload my plate or seem like I'm trying to outperform everyone (which is probably a silly thing to worry about, but that's me).

Hopefully this helps.

I don't think there's any law staring that you can't take on more than one mission, but I think the general rule is that you should finish the ones before them first.

Badfic in the Claimed list are moved back to Unclaimed after 18 months or so, IIRC, because most people tend to forget about them after that amount of time. I imagine that if you're planning to mission them and other stuff prevents you from doing so right now, re-Claiming them is kosher, but I'm not sure.