Your breaths, don't hold them. Deadline is reporting that Robert Zemeckis, Bob Gale and Alan Silvestri are in talks to adapt Back to the Future for the Broadway stage. Early talks. And that's all the news there is.
A Back to the Future musical would be interesting if you did songs in different styles according to time period. All of Marty's songs would have a 1980s metal or new wave feel, while most everything else would be Grease-esque. Hell, if they jammed all three films into one big show they could have a huge gamut of song types to run.
But this is so early and speculative that there's no use in really even considering it. I'm ok with a stage show, as long as it isn't some sort of Trojan horse to get the franchise back on movie screens. I do not need a Back to the Future reboot or a Back to the Future 4. Leave well enough alone.