In 1993 ?
15 years after, I am not sure Atari could have been saved...
The problems came years before. I would go at the release of the STE, which should have realle been a STEnhanced (68020, new graphics mode with at least 256 colors).
The STE was a nice succes (at least in Europe), but was too close from the ST, then the PC (and in little measure Amiga) take the lead. And game companies left the boat.
Even for the Falcon, this was too late, no big thrid-party games, but a lot a new small companies. This was refreshing, but not enough to make the Falcon a hit.
This was the same with the Lynx and Jaguar (small third-parties, sometimes with really good games like Super Burnout during Jaguar lifetime, or Battleshere after Atari fall). No big titles = no public success.
So, a better STe would have keep game companies (at least european) into Atari neighbourhood. Bringing these companies to the Lynx (remember of Nintendo third party politic, these company would have love to work on console market, being unable to work with Nintendo). I would not have cancelled the Panther, which would have been close from th STE, but better. Convince 3rd parties to jump into Panther train.
Then come the Jag, 3 or years after, really and completely developped, not rushed.
OK, but the test is taking the 1993 situation, not the 1989 one

Excluding an alliance with 3DO, Sega or Sony (which could have been a good option)...
The major error of the Jaguar launch was to rely on viral marketing (no real advertising, test market, Atari thought people were waitin gafter them and would do their job by looking for information on the JAguar... Sony bought the market and won by KO)
A new console need games. Japanese developers would probably not have follow Atari. American and European had the choice between 3DO or CD32 (most of old Atari/Amiga developpers were more confident into Commodore than Atari). So the 1st thing would have been to restore good relationships with computer game developpers, and encourage them to jump into console world on Jaguar. This have partially been done (remember Ubi Soft and Rayman which was Jaguar exclusive). Encourage newcomers to join the Jag (free dev kits ?)
More games, more quality games (coming from PC rather than ST - Wing Commander anyone ?)
Concerning game development, better tools (put more money and time on this part) a better support to developpers. Newcomers welcome, but they need help. Most of them failed because they weren't help by Atari.
And probably fail like Atari did...