Every full-chord position is movable up or down the neck. If there is an open string in the chord when playing in the first position, then when the chord is moved up the neck (say one fret), that "open" becomes a note at the first fret. An all-notes-fretted C, say, moved up one fret becomes an all-notes-fretted D flat, with no changes in the relative positions of the fingers.

If this conversion of an open note to a fretted note makes the position impossible, you have two choices: Either play so that that string is not sounded, or find another chord pattern up the neck that makes that named chord.

I hope what I've said is intelligible.

Dave Oesterreich