I found a short route by the summit of Mt Whitney with fun moves and lots of exposure. Could be nice for parties that finish one of the classic routes to the summit and have some extra energy. I find myself popping over a fun overhang into sight of the Mt Whitney summit shed less than a hundred feet away. Very interesting rock structures.
Over 600 feet length of climbing with about +360 vertical feet up. Could be done at 4th class, but get more exposure and entertaining moves if solid to at least 5.4. Not sure how it protects, so maybe best if comfortable soloing up to 5.6 on positive holds. The farther stay back from the edge, the more toward 4th class (? or 3rd class ?).
The climbing I tried follows the "edge" of the slope which runs SouthWest down from the summit. Simple way to find it is to hike down from the Mt Whitney summit on the main trail to reach the notch between Mt Whitney and Keeler Needle -- GPS latitude longitude approx (N36.5759 W118.2939) -- just under 0.5 mile distance.
Idea is to climb on the edge of the top of the vertical wall which faces SouthEast from the summit mass. Starts with scrambling on slopy stuff just above the edge. Late the holds get more positive out right at the edge, and then _below_ the edge. Choose as much exposure as you want, the rest of the way to the summit.
Of course which rocks to stand on or grab is an important sequence of choices, with a multi-hundred foot free fall as a possible consequence.
P.S. Much closer to the Mt W summit and much more interesting climbing than going to tag Mt Muir as add-on.