What you would have needed would have been:
1: for Kurt Cobain to have not met Courtney Love or for both of them to have checked into rehab far earlier than she did OTL, and stay clean. This will mean a hiatus between the recording and release of
In Utero and the supporting tour. This also means that either Foo Fighters never breaks out or else Nirvana has to replace its drummer for the second time in less than three years. Cue the Spinal Tap jokes.
2: Scott Weiland to have checked in to rehab shortly after
Purple. If the Stone Temple Pilots have no need to replace him because he's too stoned to do concerts or even show up at the studio, the problems with
Tiny Music,
Number 4, and
Shangri-La wouldn't have happened and probably Velvet Revolver would have been butterflied away too. Maybe
Chinese Democracy gets released in time to be used in (meaningful) protest against the Shrub by Guns 'n Roses original lineup.
3: Soundgarden not to break up after releasing
Down on the Upside.
4: Either Epic doesn't screw over Pearl Jam as badly as it did, or else Eddie Vedder's attempts at creating his own label meet with better success earlier.
5: Reprise Records screws Green Day over as badly as their orginal label Lookout, or else Lookout treats them right, but either cannot cut enough records and burn enough CDs to bring them mainstream, or else Lookout is bought out in a hostile takover by a major record company who then treats Green Day like $#1+, causing them to throw up their hands at mainstream success and concentrate on Sticking it to the Man(TM)!
6: Sum 41's members to be denied visas.
7:
Rolling Stone,
Spin, and
Kerrang! slam Oasis' first two albums as unlistenable due to their heavy handed volume manipulation, and their fortunes outside of the United Kingdom sink like a stone. As a result, the only Gallagher brothers anyone's ever heard of on the left side of the Atlantic are in stand up comedy, and the current
loudness wars are either nonexistant or else far less developed.
8: No Doubt breaks up either due to Gwen Stefani taking
Rock World's review of their debut album of "mearly Madonna with a backing band that doesn't know how to play their instruments" personally, or else later during the problems between Stefani and Tony Kanal, with bitter court battles between her and the rest of the band over the songs that would have gone into OTL's
Tragic Kingdom.
Of course, that only means that Grunge only gets a longer time in the public eye. But if it can live as long in the mainstream as hair metal did before it, and outlast the advents of Nu Metal and the third and fourth waves Pop Punk, what happens after that is purely the realm of speculation, and perfect for this forum.