I wanted what you could call a merc character.
I figured doing a quest from the city lord, and the guild master, or a village elder, would raise relations with that faction if you completed it for them, so I planning on getting relations with some factions up, by doing quests for them. But it only raised it with the person, not the faction. If I had good relations with the lords of a faction, I would think that would improve it with the faction as well.
I can also see the downside:
What if you join the faction? Say you have a high relation with your faction's enemy. When you join a faction, the relations go from 0 to -3. Making you an enemy. I'm 100% sure it should be no trouble to auto take your relation to -3 when you go to war, so that's no problem.
I also know high relation with one elder/lord/guild master does not make up the whole faction, so what I suggest would be something along the lines of a certain number of places. Here is my suggestion:
To raise relation with a faction (Nords, for example) without actually joining them:
1. Must have a positive relation with X number of lords (five or more maybe?)
2. Must have a positive relation with X number of towns (this should be different - with factions having few towns, you should have a relation of 5, maybe 10, with them. And it would also be easier to do it with towns, as they have the guild master).
3. Must have a positive relation with X number of villages (not much, as it is sometimes hard to find quests from these, and there are too many villages to try and get good relations with all of them).