Pretty simple question.
Is there a way to improve your companions' reaction towards you, after you've picked them up?

Specifically I'm using Sogg Mead Mug, and he's only Neutral [47] towards me. I'd like him to be a bit friendlier, since if I tell him to wait, and I'm gone long enough for him to wander back to Shrouded Hills, he goes down to Hostile [-5] and attacks me the moment I enter the Shrouded Hills tavern.

EDIT:
Additional reaction related question:
Ogdin Big Fist loves me (170 reaction), but when I get the key to Thorvald's house from him, he drops down to Dislike [9]. The only thing that saves me from getting assaulted by him is my Smoking Jacket. Why? We were friends... I gave him a book. What difference does that key make?

If you're not using the Unofficial Patch, it's highly recommended. I would go so far as to say "essential".

Only two ways besides quests that I can think of to raise rep with party members. One being to raise your beauty stat (ick) or, a more extreme measure, have said party member get killed and cast Resurrection or use a Reanimator on them. Bringing them back from the dead puts them at 80 or 90 rep if I remember correctly.