What's the criteria of becoming the most famous merc. company?
I think the final objective could be something a little further, like turning your merc. company into a politically autonomous order like Knights Templars, with enough influence to dictate a king/ruler/religious leader of your choice once you have gained supreme favour with your choice of faction, to make the historical mark of your order permanent.
It would be nice to have a mechanic for bids for recruitment from two opposing armies to have your order support either side.
Another extremely nice feature could be to cause wars or rather, sabotage peace efforts with bribery or covert combat missions.
Just imagine, your spymaster reports that X and Y are going to war and you can immediately dispatch recruitment offers to both, measure either side by criteria like their army size, political influence, political connections, lands owned, amount of money they are willing to pay. You can offer or demand changes (bonuses) in either category along with money. Or the spymaster reports that X and Y, currently officially at war, are going to make peace and you can do covert missions yourself or use your influence and wealth to bring other political factions into the picture to sway the peacemaking efforts.
Think of it like research in X-Com. Instead of a one-way research tree, you have a political influence tree that can go both ways. When you negotiate terms for recruitment, you can demand +10 political favour with X line of political factions, simple interactions. Winning or losing a battle could sway any number of these factions in any direction. When you have either the majority of factions or the major power players (determined by total amount of lands owned, landmarks held, goods produced, army sizes, distance from the current subject in question, religious/historical/ethnical offices/influences held) under your influence, you could instate permanent changes in the politics tree.
Ultimately, if you piss too many factions / major power players ie. plummet too much in your political tree, they will come to give you a good buttrape. But of course, first you would need to accumulate enough wealth to buy your own land and build your own castle so that you could defend it should it come to it.
Seemingly complex interactions for varied gameplay through simple mechanics. Perfect game concept for simplicity multiplied.