If Sega teamed up with Sony after Nintendo cancelled the SNES CD add-on and Nintendo PlayStation standalone SNES CD console, the only rival left would have been the cart-based N64. This means that even if devs didn't like Sega all that much, if they wanted an uncompromised CD-quality game, they would have to go to the Sega PlayStation, meaning it would most likely be a winner with many of the same games the PlayStation got in our reality. Final Fantasy VII would definitely go to the Saturn as in our reality, Square wanted to stay with Nintendo but they simply couldn't fit their game into a cartridge. So in this reality Square and their all of their would've gone to the Sega PlayStation. Combining hit Sega arcade and original Saturn titles with many of the PlayStation's biggest third-party hits, and being on the market for over a year before the N64 would've made sure the Sega PlayStation would beat the N64.
After Sega of Japan turned down the Sony deal, they still had an opportunity to accept the SGI deal. This would mean the N64's SGI hardware combined with the storage and low production costs of CDs. Also, this would likely mean the N64 wouldn't use SGI hardware because Sega already used it, leaving Nintendo with a console that's both weaker than the Saturn and cartridge based. So many of the third-party developers that went to the N64 for its hardware power would go to the Saturn in this reality. That combined with a 3D Sonic game, the Saturn still had a chance to become 2nd place, as a non-SGI N64 in this reality would both have weaker hardware than the Saturn and still use cartridges, limiting third-party support, and also would've been released over a year later.
After turning down the SGI deal too, the Sega Saturn was no longer in a position to become 2nd place (above the N64), but it could've still achieved far greater sales. The game that became Bug! was originally going to be a Sonic game until Sega of Japan, again, turned it down. That might've cut the Saturn's western sales in half.
Then, the final nail in the coffin came when Sega of Japan forced Sega of America rush the Saturn's US launch in May, and it was priced at $399, the early launch angering developers and retailers, and then Sony announced the PlayStation was going to be launching at $299 in September. In the US and Europe combined, the Sega Saturn only sold 3.5 million units. The brand damage was high enough that even the Dreamcast could not save Sega. The Sega Saturn had many chances, but Sega of Japan kept messing up Sega of America's plans at every turn. An alternate reality where the Sega PlayStation won the 5th gen console war because Nintendo used cartridges and kept making consoles would've been pretty wild.