As far as whatever I have experimented with this issue, I keep the root note same.
Lets say some prog is being played on C major scale. Like C maj -> A min -> G major -> C major
I would start by playing in C Ionian (major scale)
and mebbe shift at a point of time to C Phrygian (which imparts certain spanish music touch)
Cahnge to C Lydian for a "cool" "spacey" sounds (like Satch n Vai use sometimes) an dswithc back to C Ionian.
Now if you question is HOW to change from C Ionian to C Lydian or C Phrygian etc ... you need to be aware of the common notes.
Otherwise you can alos use the chromatics are bridging notes.
However, somehow, I have not yet mastered the use of chromatics as passing notes. :(
You donít get what you deserve, you get what you negotiate.