Hi,
A common alteration on the major chord is to add a #11.
The formula of a Cmaj7#11 is 1 3 5 7 #11
#11 is to raise the 4th degree by half step.
4th in C is a F. Raise half a step is F#.
So the chord tone in a Cmaj7#11 is C E G B F#.
You can easily improvise over the Cmaj7#11 with the C major Pentatonic or Lydian scale.
Have Fun!
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