Here's some (very) speculative rambling about what a Grey Majority EIC would mean.
First, it cannot be a normal for-profit company. Reinvestment is ok, but there's a limit to that before people start getting upset about a economic takeover. There's some room for silk sheets (good nights sleep is a totally practical), but not to the degree a fully developed EIC would produce, even setting the silk aside. At some point, it has to reach mostly neutral income.
Second, it cannot remain a normal private company. We already had someone come in about what competition given the grey stockholder means. With the official heiress a Grey and with a Grey stockholder majority, people will consider it a Grey College operation, or demand a redistribution of stock (which could be done, but I don't want to, and so it will not be discussed further, for it is icky).
I suggest embracing that, and making it the official Unofficial Stance. The EIC essentially becomes a government organ, with two major roles:
- Infrastructure: Those useful services that you can't profit on without removing much of their use. Postal service, fire brigades, public transportation if that ever becomes a thing. That sort of thing. It works for people, who get a useful service at a reasonable price. It works for the government people, because you really want that sort of thing, but you also don't want to finance it, because the benefits are kinda indirect. It works for the empire in the long term, because the support won't be cut by shortsighted/selfish local nobles. And it works for the Greys, because it gives them the perfect kind of soft power: Normally unobtrusive but quite powerful, and non-threatenting. Annoying the postman is a very bad idea, but being the postman doesn't let you conquer anything, and so people aren't tempted to conquer you first.
- Creating a healthcare system would be a great way for Eike to life out and apply her Shallyian faith.
- Base-level supply of common goods. If the EIC sets an upper limit on the cost of food and such, that means profitieering is strongly curtailed. Which seems like something the Greys would approve of. It already served that kind of role before, supplying the army of Stirland during the Sylvanian campaign. As a organization belonging to the empire as a whole (by way of the Grey college) and sworn to political neutrality, it can actually take on this logistic role for other provinces as well. As a neat bonus, it makes inter-province fights more difficult and costly, because then you wouldn't benefit from that logistic network. This is also something the Greys would very much like.
- A variant of this and the first, the EIC could also act as a middle man for smaller traders in general. For a small fee (and following some behavioral principles), you can have your stuff transported and sold to distant locations. This is also already sort of happening, with traders joining the much better armed EIC convoys due to the rise in riverine piracy comming from Marienburg.
That would also be force towards the reduction/removal of internal tariff barriers.
You'd still have the dwarf trade and other such things that would get you a good profit, but that money would go towards endeavors that aren't really profitable.
I've also considered that the EIC might take on the role of something like the Empire's Merchant Marine (especially if Marienburg goes well), and handle trade with dwarfs (and elves, again if Marienburg goes well). That fits the Grey role of diplomats, but it also seems like it'd be a bit too much, powerwise. And it just doesn't have such a good basis in the quest so far. But it is another possibility. Maybe after the runestone project, because that's pretty international.
Thinking about it, the EIC in this scenario would be a force for the centralization of the empire. It would actually be uniquely well positioned for this. The Colleges are one of few (the only*?) organizations that by their charter work for the empire instead of individual provinces or rulers. And the Grey college specifically is obligated to political neutrality, so a Grey controlled EIC doesn't pose the risk of losing power to a rival.
*Are there any others? The cults aren't, because they're both too local (Ulric is more a northern thing, Sigmar more a southern) and not local enough (Myrmida and co exist outside the empire as well, leading to... uncertain allegiances). The Witchhunters are sort of in the correct direction, but we already saw in story that they had problems too whether to serve Sigmar's church or the Empire. Their mandate doesn't lend itself to it either. The Emperors will push towards it, but they also have a lot of other ambitions, and they also have the Reikland (or another province) as their personal fief, which means they're not impartial. Such attempts will also get more resistance from the electors because of that reason. A lot of other imperial institution will have a similar problem, because their loyalties would be to the person of emperor before the state.