This is too tough to even think about. Maybe, after losing the title to Steve Austin, he would resume the feud with Undertaker. It was obvious that Kane had been used like a tool from then on, so maybe DX could have tricked him more, by faking and pretending to recruit him, and trying to take Undertaker out. I just couldn't see the rivalry between Undertaker and Shawn Michaels ending in the casket, especially with the huge ordeals they made, about nailling the coffin shut on him and his character.
Also, since Stone Cold was destined to be the face of the company, maybe he would have lost the championship to Shawn Michaels for less than a day, at King of the Ring, instead of to Kane, then have taken it back the next night on Raw is War, giving Shawn another reign with the belt, not that he needed it. Other possibilities, maybe thought of at the time, could have involved Shawn Michaels versus Mankind in a feud longer than a month, with Shawn taking the place of Kane again, who definitely didn't seem to be in the top three sections for sales or fans.
Edit:
Giving it a second thought, I wanted to expand a little bit. I found Stone Cold to be a very boring champion, and was even more apalled at that hideous tournament for the Deadly Games at Survivor Series, with the crappy Rocky Maivia winning it. If Undertaker and Kane, with the double pin on Stone Cold led to the title being vacated, maybe they could have planned to have done a mini-tournament with Kane, Undertaker, Shawn Michaels and Steve Austin instead, after Stone Cold still doing the non-count while refereeing Kane versus Undertaker for the vacant WWF Championship at In Your House: Judgment Day. It would be something similar along the lines of that smaller competition at WWF Vengeance 2001 with Kurt Angle, Chris Jericho, The Rock and Steve Austin. I know there is no way at the time, for people to plan it out, but it was a better theoretical scenario than what actually occured, with nearly SIXTEEN freaking lax bruisers competing on the show instead, with the likes of Gillberg, Steven Regal before he evolved into a technician in the ring, Big Boss Man, and even Jeff Jarrett involved for the championship.
Anyway, it would have been interesting to see if Shawn wanted to upstage Hulk Hogan and Bret Hart, or at least rival them in terms of numbered reigns with the title.
I am so glad, though, that The Rock and Shawn Michaels were not involved in a feud longer than one show (referring to WWF Smackdown! in August of 1999, with Shawn giving Rock the super kick). They wouldn't mesh together well, at all. Rock was way too overrated in the ring, as far as technical skills went, though without a doubt, he was probably among the most energetic and explosive wrestlers in the history of that industry. Even worse, the casual, smooth yet sassy talking Shawn Michaels, even trying to comprehend slang and urban attempts at the American language in the form of lame outbursts from The Rock, would have been nearly pointless. It is such a shame that Shawn didn't use more backstage power to hold Rocky down, while he was the Commissioner in 1999.