Shoot, you guys - five pages in one night that I don't really have time to read at the moment.
Noting that we're trying to figure out Parasol/Ballpoint, I'm going to post what I wrote down in a notebook last night for my own reference.
Parasol Corps:
Parasol's core focus is its departments of Research & Development. Their goal is to research and develop !!SCIENCE!! so that Parasol as a whole can uncover the greatest secrets of the interuniverse. Their secondary, much lesser focus is their mobile infantry, which they use to comb through alternate dimensions to uncover new areas of !!SCIENCE!!, and protect experiments already in progress. Though their weapons technology is behind that of Ballpoint's, due to Ballpoint's scavenging ways, they make up for it in combat by employing their seemingly non-destructive inventions in a clever, strategic manner that not only levels the playing field, but gives them an edge. When Parasol finds something marketable, they choose the proper universe/timeline/time/location and sell it, trading solely in interuniversally rare metals. Through this they earn their income and expand.
Ballpoint Tech:
Ballpoint Tech is a mercenary-style organization. Most members are called "contractors" and are given standard-issue gear at the time of their employment, though they may use whatever weapons/armor they desire. They are allowed to hire themselves out for their own profit while off-duty if they so wish, so long as it doesn't detract from the well-being of Ballpoint as a whole. While on-duty, the contractors are under the command of higher-ranking employees, and form a relatively large army. The organization uses divisions of this army to better itself and its equipment through blitzkrieg-style raids, looting technology and valuables as they go. On occasion they market their weaponry to neutrals and allies through the interdimensional black market, though they trade honorably take care not to make more enemies than necessary. Through this they earn their income and expand.
Just my thoughts on everything. I may have missed a page farther back where people decided unanimously on what everything was, and if so... whoops.
@Splint: Normally I'd be all for aerial technology (more for it than most things, I came close to being a pilot, and have semi-passable knowledge on flying helicopters), but both of them become undefeatable if Spearbreakers was ever to come out of its shell and attempt to combat the companies.
EDIT: As far as I see it,
Eris is an underground entity that operates covertly.
this sums Eris up perfectly, but I'd add that they accomplish their means through manipulation. Kind of like ninjas that like getting into your head and using you as a puppet to take down your own allies, and get you killed in the process - all without being noticed. In my opinion, that's freaky scary to have to go up against. I'd rather see my foe.