I thought I'd try to test the maximal storage capacity of Sir Willibald's cardboard boxes + the Core box. As it turns out, you can carry quite a lot!
(TL;DR: 2-3 VSD's, 5-7 Neb/Corvettes, and up to 45 squadrons. Or any combination thereof..)
The first layer: 2 VSD's, 2 CR-90's, 3 Neb-B's (all with associated gearboxes), various upgrade/damage/ship/squadron card boxes (a full set!), and my token tray.
Next, the fighters! I squeezed in 30 squadron boxes.
(sorry for the blurry photo)
Now, if you took out the token tray, you could definitely squeeze in another 15 squadrons. And if you take out the various upgrade card holders, you'll have enough room for another medium sized ship. You've got lots and lots of options...

