I use a capo both on the Gibson K-1 and the Eastman 805. Playing in the key of A, and using "E position" (the mandolin equivalent) chords, bothers me, so I capo two frets and use "D position" chords. I use a lot of open strings, so I'll capo to get to a point where I have drones, open bass notes, etc.
Haven't tried alternate tunings yet, though.
Gibsn: '54 F5 3pt F2 A-N Custm K1 m'cello
Natl Triolian Dobro mando
Victoria b-back Merrill alumnm b-back
Stradolin Vega banjolin
Sobell'dola Washburn b-back'dola
Eastmn: 615'dola 805 m'cello
Flatiron 3K OM