A common improvisational move in jazz is to incorporate approach notes 1/2 step below and a whole step above chord tones. Take a simple G major chord and mentally mark off the notes 1/2 step below and a whole step above the G B and D notes.
The result is this pattern that features 3 notes per string and shadows the basic elements of the G maj chord. We end up with the added intervals of the maj 7, 9th, b5, 13th, and the #9 and as you might suspect is useful when encountering both a plain major chord (good for adding some unusual flavoring) and if you mentally continued the process by following the A with a Bb and the E with an F (not indicated on the chard below), you'd end up with a familiar synthetic construct that works swell over dominant chords with the addition of the F note (b7).
Try experimenting with visual shapes and not just finger patterns. Those can be useful and fun but you can just as easily fall into ruts with them. Get geometrical or play “connect the dots” in unusual ways:
This idea works well in most musical contexts and, as you encounter complex and extended chords, the possibilities get increasingly wild. Don't be afraid to whip some of these ideas out next rehearsal. I use these approaches all the time to add an quasi-exotic flavor to standard rock progressions. Anyway, here is a couple of good licks that incorporates similar ideas: