Hi Steve,
I've not personally tagged Mt. Muir, but I have seen several photos of other folks making the climb. Mt. Muir is not far off the trail to Mt. Whitney, but the climb does involve lots of "exposure". Of the people I've seen climbing Mt. Muir none were using rope/harness/protection, but my guess is that many folks would prefer a bit more security.

With your experience I doubt you will have a problem with the extra distance/time, and the only consideration might be your comfort with exposure.

Scroll down to see pictures at the following link:
http://www.whitneyzone.com/wz/ubbthreads...Photo#Post31205

Good luck,

John