guitar
C major

Below are some ideas / reference material for soloing over a C major chord. Wherever "pentatonic" is indicated, I am refering to a "minor pentatonic".

A pentatonic
D pentatonic
E pentatonic
B pentatonic - contains #4, will impart a "Lydian" quality

C Ionian mode (C major scale)
C Lydian mode (G major scale) - contains #4 - more open sound

G maj7 arpeggio -contains 9th and #11th


....for more "outside" ideas.....

A minMaj7 arpeggio - contains #5
E major triad - contains #5
D major scale - contains b9 and #11
Gb pentatonic - contains b9 and #11