Bear with me, this does come together. Sort of.
Thought two. In cyberpunk games the setup tends to be player-characters versus the evil corporations. I can see why; the source fiction supports it, faceless corporations make good villains, as the real world shows us -- ooh, politics! -- and it's a fertile ground for adventure and conflict. What you don't tend to see is players as corporations. I'm sure there's a Shadowrun sourcebook for playing as a corporation, because there's a Shadowrun sourcebook for everything, but otherwise the only instances I can think of are the card game Netrunner, which puts one player in the role of the corporation, and the computer game Syndicate, in which the player takes the part of the COO of struggling Eurocorp, in a setting in which corporate disputes are resolved with minguns and rocket launchers.
You can see where I'm going with this. How about, instead of the usual cyberpunk setup, or even placing the player-characters as corporate agents, letting the players be the corporation itself? Let's take Syndicate as the basic structure, with the players taking control of a minor corporation's business affairs. We could split the gameplay into two main phases.
The first would be a "boardroom" -- for lack of a better word -- phase in which projects and research are funded, intelligence on rival organisations is gathered, and shareholders can demand certain actions. We could probably cannibalise Mutant: Year Zero's ark mechanics for this.
The second part of the game -- which I will call the "street" phase -- would be more traditional, with corporate agents -- the player-characters -- going out into the neon-drenched city to disrupt the schemes of other corporations by recruiting their employees, stealing their plans, and eliminating their agents. Perhaps there could be some sort of resource mechanic that puts a limit on the mission; once the situation on the ground becomes unprofitable the team is ordered to pull out, unless the players can convince the board to extend funding. Maybe that's too spreadsheety.
The end goal would be up to the players, but becoming the pre-eminent corporation is the obvious one. I wouldn't want to delve too much into the business side of things; the idea is to provide some background and structure for the adventures, not to spend half of every session going through an accurate simulation of corporate economics.
If your group isn't into cyberpunk -- I suspect at least one member of mine wouldn't go anywhere near this in that genre -- then the same kind of structure could be applied with ease to something like Eberron and its dragonmarked houses, or a colonial setting, whether it's the East India Company or the Eastern Galactic Arm Company.
Would anyone play this? The fact that Hostile Takeover: The Faceless Corporation RPG doesn't already exist suggests not, but I think it could be fun.