Audi offers an
active rear differential that can vector torque left/right with minimal loss. They call it their "sports diff." I had it on my S4 at it was _amazing_.
It will simultaneously push with the outside rear wheel while retrograding the inside wheel, creating a moment of inertia rotating in the direction of the turn.
Felt like the hand of god reaching down and helping push the car around corners. Awesome on the track, and daily driving. You could punch it while exiting a turn earlier than normal and the car would sort it out without having to cut engine power or fire the brakes. Really defied physics.
So, torque vectoring left/right
is possible with only one engine. Downsides are it was larger, heavier, more expensive, and more maintenance prone than other types of diff.
Here's a nice video explaining the difference between torque vectoring front/back with an electromechanical differential lock (EDL) I.e. brake based diff lock on an open differential vs. their active "sports diff."