Just looking at modern game design, this is certainly a doable concept. I was brainstorming the concepts that make SR work, and how other games have been developed recently that all work in tandem.
1. Missions are essentially Heists
So GTA Online incorporated Heists a few years ago, and the concept would work well as a building block for SR Missions.
You can queue up for a random group. Select a role (Melee, Ranged, Magic, Rigger, Decker, Etc) and wait for the Mission to be launched. Hang out in a player's pad until it launches. Of course, you could have both fully pre-packaged missions as well as randomly generated ones, instead of re-running the same missions over and over again.
2. Open world exploration of 6th World Seattle would be amazing
Just look at game demos of Cyberpunk 2077 for a general idea of how far along gaming has come.
3. First player stories are no longer a forgotten concept
Along with random/free missions, a storymode can be incorporated. Just look at Star Wars: The Old Republic, where each class had a unique storyline to go along with the regular quests, etc.
4. Random encounters would be incredible
5. Loot concepts are already built into the core game.
Loot a weapon? Awesome. Loot a weapon with more attachments, in better shape? Weapons with incredibly high availability ratings?
Loot cyberware - got Alphaware Wired Reflexes Rat 1? That boss had Deltaware Wired Reflexes Rat 3.
6. No classes. No levels.
Street cred baby. Much like "gear ratings", your street cred would determine unlocks, etc.
See Star Wars: Galaxies for how much players actually LOVE classless MMOs.
Gear+Cyberware (Or Spells) + Customization of skills - It won't take too many options before you start seeing incredibly unique builds.
7. Reasons for subscriptions.
Want a F2P game but still encourage people to get subscriptions without giving them more powerful characters?
* F2P - Poor Lifestyle. Your apartment is small and you have fewer options to customize the look
* Purchased from the game store - Medium Lifestyle
* Subscription - High Lifestyle
* Purchased the Gold Edition (or whatever) - Luxury Lifestyle
8. Guides will be Immortal Elves; GM's Dragons
... Nah, but still

9. Edge would be used to activate special abilities to account for the MMO concept
Edge would, instead of generating dice re-rolls, could account for:
* A quick "respawn" at 1/4 health
* Increased/Automatic critical hit
* Traded at the end of missions for boosts to loot
I, admittedly, have no idea what it would cost. Probably a minimum of $150 million, so this is almost assuredly a pipe dream. Still, the idea of my Elven Sniper Weapon Specialist running with my wife's Covert Ops and a few friends from across the country? I'd be all in.