This might be a good idea, but it might have an issue: Whereas people can't merge, companies can, and this might incentivize mergers. It'd have to be thought through.
The tax paid is an increasing, convex function f of some measure x of "profit". I'm not sure how to normalize by company size (or if you should). First, let's say x is per-capita profit, "capita" being the number of employees. Let's also say that the tax f(x) is also per-capita.
Now say there are two companies, 1 and 2, and for simplicity say they each has a single employee, the owner. They would pay a total tax f(x1) + f(x2) to the government, on a before-tax profit of x1 + x2.
If those companies merged, then they'd pay a tax 2 f((x1 + x2)/2), again on a before-tax profit of x1 + x2.
You can just divide both sides by 2, the total number of people involved, to get the usual statement of Jensen's inequality:
(f(x1) + f(x2))/2 > f((x1 + x2)/2)
Thus, with my choice of per-capita normalization, this tax scheme incentivizes mergers. Probably it also does so for other normalization schemes. (What are other reasonable denominators?)
This incentive goes away if the tax isn't normalized at all. In fact, then it mostly just disincentivizes largeness. Which, on the surface, might be a good thing, given that we have too many monopolies. On the other hand, it might incentivize some kind of artificial splitting of corporate structures (not that this isn't a common thing already, what with "Double-Irish Dutch sandwiches" or whatever they're called).
Possibly anything that isn't linear will be gamed in some way.
And, not to sound like an apologist for the capitalists, but it's true that when they take their profits out of their companies, then they will be hit by convex taxes which are a little harder to game (though there is still marriage and other things). And that doesn't prevent companies from amassing stockpiles of cash -- representing power for their owners -- without paying out.
I like this general direction, but it needs some "red-teaming".