It’s definitely possible; I’ve met someone who has done it! There is an outdoor industry group that has an annual team competition to do exactly that. There are teams from A16, Keen, REI, etc.
They start with Baldy going up and down the Ski Hut route (the shortest route). Then they go on to San Gorgonio via Vivian Creek (also the shortest route).
Finally, they take the tram up and make a beeline for San Jacinto. The real beasts are able to make it back down from San J. in time to catch the last tram of the day, but technically they just have to summit San J. within 24 hours.
And while the thought intrigues me, I’m not in condition to tackle that challenge right now. I’d have to do some serious training!
A few tips from those who have done it. They have three daypacks and three sets of shoes and socks. Each pack is stocked with water and food, so they have one less thing to worry about. And putting on fresh socks and shoes between each hike? Awesome.
If you find any takers, let me know. I’d love to do a story about your adventure! I know one guy who might be crazy enough to try it… I’ll see if he’s interested.