They've stated before that it is unlikely they will ever expand the assignment slots due to balance issues. I'm not really sure what those balance issues are but I'd imagine it'd have to do with hardcore doffers vs. the casual ones or ones that prefer to not really mess with it.
I have said before that more assignment slots would be one of the few things I might be willing to spend some actual cash money to obtain.
However seeing as PWE appear willing to sell their own grandmothers if they thought it might make a few extra bucks (practically EVERYTHING else is upgradable for cash) I suspect there must be a bloody good reason they won't do it.
I suspect the OP, like me, is still some way off being Tier 4 in all departments (I am T3 in all but 2, Exploration is still T2 and Engineering is T4), once we get there our desire for more slots will probably evaporate.
Well it does serve as a time sink. I'm nearing rank 4 in all of them and with a couple maxed at 150k. I've been at it since... start of March or April. I forget. So it takes a few months to max them out(with the 10,000 cxp bonus galore, and bonus cxp weekends also in the mix) I would like to see them bumped to 25 at a time, though. I don't suspect that would wreck things too badly. It might shave off one to two weeks at best. I'm just tired of aborting the "least important" assignments when that uncommon-very rare assignment pops up that you can't miss out on, like recruitment or Gamma Quad trading.
Here's what I do. If I know I'll be sitting in front of the game for an hour or two, I'll load up on the short assignments that are an hour or less. Thus way the progress while I'm cruising the nebula's and expanses working on the chains. When I know I'm going to be logged off for a while, I load up on the longer assignments. And if you find you've got 20 assignments running and 5 minutes until a handful finish, do an STF or Alhena, or some other daily. It's cool when 4 or 5 fifteen minute assignments all finish at one time.