There is a way: simply focus on certain jobs and ignore the rest. It's against the idea of the multiclass that the game offers but hey, not our fault if the game isn't properly fit to accomodate our inventory issues right?

I mean, I have 3 tanks at 60 but I only use one (my warrior). I have my Astrologian at 60 and I'm not gonna bother gearing up the other 2. I have various dps to level up but I'm going to stick with the monk and MAYBE machinist. Or else just my monk.
All the rest are going to be ignored: that's a lot of space going to be saved and I have only 3 jobs to focus on. If I tried to focus on the rest, I would need more space.
Well that, and the fact that you can properly gear up only few jobs because "weekly" locks. Way to make the multiclassing meta!

Desperate times call for desperate measures is well fit in this situation.