On the other hand, I could see this quickly turning into The Rogue Trader Wars: Act I. While it is entirely possible that the other rogue traders will band together, nothing is stopping the more extremist or puritan rogue traders from banding together against them.
I could see it turning into a huge clusterfuck fairly quick, however, with rogue traders calling in favours all over the place, and once Lord-Admirals, Inquisitors and Chapter Masters start getting involved, someone is going to get an enormous beatdown. Peers of the Imperium being at eachother's throats is rarely a popular thing.
I think that the fact that such a war would hurt profits (and Profit Factor) of all involved would help to keep it from getting out of control. I see most RTs as having a gentleman's agreement with guidelines on what levels of conflict are acceptable. RTs that go much beyond those limits (loose as they are) will become pariahs and are a danger to the profits of all.
The same could be said about any war throughout history, really; but it never stopped anyone. The winning party would no doubt raise their profit factor, and there's definitely the prospect of eliminating rivals, opening the door for monopolization, not to mention those precious, precious assets other rogue traders have that would be ripe for the taking.
That said, however, Rogue Traders do - at the very least nominally - have certain obligations. In the case of the OP's Rogue Trader, he's out there to clean up the Koronus Expanse and - for what it's worth - bring those peers that may have strayed from the light of the God-Emperor to "justice".
As much as much of the appeal of Rogue Trader is going buck wild and flagrantly ignore half a gazillion rules and regulations of the Imperium proper, there just *have* to be a fairly large number of them not into it for the money, that is genuinely out there in the expanse, not for personal profit or for dynastic gain, but to serve the Imperium. Old Chapter Masters of the Space Marines, Puritan Inquisitors, Sector-Generals and Lord-Admirals and Arch-Adept Lucius Numberfiddler, Grand Bureaucrat of the Tithe Imperialis aboard his ship, the Golden Tax-Return.