Is it possible for a crypto company to introduce more mineable coins after all coins have been mined?
Yes, but it's impossible to predict accurately whether the users of the network will accept the change or possibly even create a solution of their own that is diametrically opposite.
You might care to reflect on the kind of relationship a company *can* have with a peer-to-peer network of pseudonymous nodes. I don't think the notion of “control” is at all supported. Your thinking should be along the lines of “influence”, “persuade”, “bribe”, “plead”, “beg”, “threaten self-harm”.
Cheers
Graham