It's not possible. The length and content of the menu is determined by your screen resolution, but eventually even the biggest screen will run out of space. this behavior has already been improved over recent years so current versions show more than older ones, but there is only so much that can be done to enforce it from the side of the devs...
Thanks for the quick response.
I've uploaded a pic to show how my screen looks:
I could understand if the screen just wasn't large enough, but it seems to cut off much earlier than necessary. I would at least expect the categories to become submenus, but AE seems to just throw the individual plugin names together.
Anyway, as it's not something likely to be changed soon, I'll start using the Effects & Presets panel to find the plugins while I'm trying them out. Luckily, most of mine are trial versions for now, so I'll be removing them soon. Hopefully AE places the plugins back from the 'Others' category when I do remove some.