In the Key of C, I've been discovering the baritone chord from Mustang Sally -- third fret, low to high -- G C G C X X
Sometimes a five-string F shape sounds more appropriate than a six-sring bar chord. Again that is a V root.
Among "conventional" voicings, you have the I V and the I III (E or A shape; and then the C shape). Whatever the other person does, you can do the other, and at a different part of the neck.