Would this limit vertical integration? E.g., could SpaceX exist under your scheme, making rocket engines, rockets, and satellites? Is that all one line of business, or is it multiple lines of business? Is Apple's hardware and software business one line of business or two (hardware, and separately software)?
It seems to me that your approach is easier to apply when a company strays from its line of business rather than vertically integrates. So a company that makes hardware, then years later gets into software for its hardware, that might be a problem, but then how could that be a problem if Apple-like companies exist concurrently.
I think all antitrust schemes are tricky and slippery. Not that we shouldn't have an antitrust scheme, but that I'm not sure how to construct one that doesn't somehow suck.