Here you go.
Influence
1 self-absorbed and unknown
2 might stumble on a fact now and then
3 can make its opinions known directly and learns of major events in a timely fashion
4 well-informed of current events in a decent sized area
5 array of sources to check against each other for accuracy, legions of advisors/blackmailers
6 the walls have ears and when you whisper generals shout (and soldiers scream)
Might
1 Poorly trained spearmen
2 Adequate soldiers with poor weapons
3 typical large city guard, small corps elite soldiers
4 good troops with excellent leadership or vice versa
5 well-honed confident superbly balanced fighting force
6 Tough experienced veterans well organized with plenty of magical backup
Sovereignty
1 Barely suppressed hatred and rage
2 grudging obedience with more resentment than initiative
3 typical loyalty including griping but banding together when outsiders make remarks
4 unusual dedication
5 commoners take actual pleasure in promoting the Company, feel pride in doing civic duty
6 total cultural cohesion to the point of xenophobia/condescending snobbery
Territory
1 A single large ship with crew
2 a town, modest duchy, broad but shallow national conspiracy
3 very small country, very large independent city, national merchant empire
4 large region in a large nation, medium sized nation
5 large country
6 vast varied nation with proud history and highly developed culture
Treasure
1 Visibly pitiful, bad haircuts
2 struggling, little in the way of fiscal safety net
3 small tightly run enterprise or large shabby one
4 prosperous organization
5 deep reserves and strong record of success
6 radiates casual opulence
You can improve qualities by 1) Combining with other companies to form bigger companies 2) Conquering your enemies (reduce two of their qualities to 0 in the same month - one must be either Territory or Sovereignty) 3) spending experience (10XP times the new level) 4) Sovereignty, Influence and Might can all be raised through Company rolls (Improve the Culture [Territory+Treasure], Rise in Stature [Sovereignty+Treasure] and Train/Levy Troops [Sovereignty+Territory] respectively). You can roleplay something to try and give bonuses to those rolls. Also, Wealth converts to Treasure at a 3:1 rating so if you loot enough temple complexes you can get some fantastic booty.
Since you've already reduced the Mitos' Treasure to 0 this month, if you attacked them again targeting their Territory you might be able to destroy them and boost your Territory. What with looted ships and ports and such.