Here's something so nutty it might actually have worked: a few years back Sega's Australian studio pitched an idea for a series of remakes called "Sega Reborn", which wouldn't just recreate classic games like Golden Axe and Altered Beast, but somehow tie them into the same, single universe.
While the idea was obviously never picked up, hitting various roadblocks between the Queensland studio and company HQ in Japan, it's certainly an interesting one to take a look at, now that...we'll never actually get to play them.
The over-arching universe would see the games, set thousands of years apart from each other, release under the unified Sega Reborn label. While not strictly remakes - they'd include new content and would make a few changes here and there - for the most part they'd follow the same progression through the story and levels as the original games.
Except for the meta story, of course, which was going to be subtle, and implemented as more of an underlying mythology (mostly for marketing) than as key parts of each individual game's plot.
Below you'll see a video of Golden Axe pitch (remember: this was a rough pitch made in Unity, not a finished product), and I've already mentioned Altered Beast, but other games that were due for the Sega Reborn treatment were Streets of Rage and Shinobi.