There are corporations in eve with a very well delineated purpose. They provide a crucial element in Eve that’s unique for gaming. I am very happy with how this functions.
There are however a few problems - players should be able to formally associate in collaborative societies other than corporations. These can be trans-alliance organizations, sharing specific goals and resources. Some of these societies can be secret, many should be NPC driven, some may be illegal, others may be governmental - but the best potential for these should be to offer resources to characters who are unable to pool resources because they are locked conceptually inside a corporation.
The simplest benefit would be to create a foundation for alts - to allow a player (and maybe a few friends in other corporations) to discretely share station resources between all alt characters. Right now the moment I enter a corporation with my main I get locked out of my massive alt corp and it’s considerable resource pool.
But specific coteries can also provide distinctive other benefits from having tailored poltical associations with NPC organizations, which can discretely filter back to members in the form of unique missions. Kartels may build complex secret transactional or political benefits that might subtly (or not so subtly) sway the effects of piracy, police patrols, random encounters in specific systems or regions. Or some clubs might gradually develop access to unique types of stations, ships, technologies or other resources.
I am not per se arguing espionage agencies or treasonous conspiracies - but this would truly be an awesome mechanism for conniving players to create secret caches of equipment here and there for their members to use. Maybe a secret base only available at a high development level for the Organization where the Group can stash certain levels of vessels - T2 frigates, maybe even eventually as big as Battleships.
The ideal situation is that these nebulous “behind the scenes” agencies grow a following of NPC’s that manifest tangibly in space. Maybe as pirates, maybe as freighters, maybe as miners. Some of these cells might even have connections with Sleepers, Triglavians, etc.
Right now new players face a suffocating amount of options and choices. I can envision key universities, academies, schools, that offer training seperate from existing corporations, each with very specific curriculums, objectives, rules, requirements or fees.
Having described the above I can see at least a dozen or so character skills that would deal with the in-game quantifiables associated with these Organizations.