Looks like we should be able to have a full compliment of those, definitely. The Yui 7 page seems to suggest we can hold a good amount. Glancing at the dimensions, they're not very large and it sounds like they're stored stacked up nicely and then plucked out and deployed automatically. Certainly something we'd be stocked up on, with our type of mission.
For anyone that didn't know, Semjax is on leave for a bit, so I'll handle their character until they return. For those grouped with Yumi, you can NPC her around you, as long as it is nothing major. I'll try for another post tomorrow, I'm about to head out of town for the day.