Some or all strings do not play in tune up the fingerboard, sometimes, they can be up to 50 cents higher on the first fret (this is a nut problem) but drifting out of tune high up the fingerboard is a bridge/saddle adjustment.

Changing string gauges will invite intonation issues.

Tip:- if the string plays sharp at twelth fret, lengthen the string (move the saddle away from the nut) obviously opposite for flat at the twelth - loosen string tension when ajusting saddle to avoid damage to screw thread.