Apparently, it is possible to encounter a bug in which the Outfitter tells you "I'm afraid you can't hold any more of that item. Might I interest you in something else?" despite having plenty of space.
Zeke took video clips showing his depleted inventory and the bug in action.
Zeke used the slowdown fix patch, but it was still bugged in his vanilla ISO, and apparently this is a very rare issue even in vanilla:
Dakitty on Discord also mentioned that they'd had the same issue once, but had suspected it was the result of using the US slowdown fix on a PAL ISO. They'd had to scrap their entire save file in order to restart on a US ISO.
Zeke, however, WAS using a US ISO.
We ended up suggesting to him to go get the Lion Editor and see if any inventory slots were borked up in the save file. He didn't find anything. But I kept trying different Google searches and finally found something that shed some light on the issue, even if the trigger for the cause was unrelated:
I suggested that given this, there might be a bug with the Nothing slot in Zeke's game - but he might not see it now that the Lion Editor automatically compensates for this bug after having previously caused it itself. I told him to save the file and try again.
And it worked!
So if anyone in the future ever comes across this rare and apparently purely vanilla bug, try a quick fix with the Lion Editor to see if your problem is that you have too much of Nothing.