I was just made Guild Master of the Thieves Guild, and was planning on becoming Guild Master of the Companions, but then the thought popped into my mind that I might not be able to become Guild Master of two guilds. So I looked it up and got nothing, and that’s why I’m asking here.
Becoming the leader of any guild in the game does not hinder your progress through the others in any way. They have completely standalone quest lines.
For all intents and purposes the "guilds" of Skyrim are:
- The College of Winterhold
- The Companions
- The Dark Brotherhood
- The Thieves Guild
Similar but separate factions include:
- The Bards College - can be joined as a sort of "helping hand" but not a student, and has no progression
- The Blades - can be joined but not led, nor is there any progression
- The Imperial Legion - there is progression but you can only reach the highest rank of a soldier and the quest line is mutually exclusive with The Stormcloaks
- The Stormcloaks - the opposite and contemporary of The Imperial Legion
The main point of intersection between a guild quest and another quest line is during the Dark Brotherhood when it overlaps with the civil war quest line. This will cause some stalling while one quest line waits for the other but the game and dialog handle it pretty well.