For a three-engine-out abort, there's a couple of great diagrams provided in the answer at https://space.stackexchange.com/a/39733/11532 showing different abort contingencies. One contingency plan is the "RTLS" (Return To Launch Site), where the spacecraft would reverse direction and fly back to the spaceport. However, this raises the question: with the main engines out, what provides the thrust for the flyback maneuver (the "power" for the PPA or "Powered Pitch Around")? For that matter, the diagram mentions "MECO" (Main Engine Cut-Out); what "main engines" are going to undergo MECO if the SSMEs are all already out? Is that the SRBs (Solid Rocket Boosters), or the OMS (Orbital Maneuvering System), or...?
The SRBs seem like the most likely answer - they've got far more raw power than the OMS, and they are steerable - but they're attached to the external tank, which I expect you'd want to jettison for weight and aerodynamic control reasons even if the lack of a balancing thrust from the SSMEs didn't cause center-of-gravity issues. They also don't have controllable throttle or shutdown (aside from the fight termination system, which basically just blows their casing apart). Additionally, you'd need to jettison the external tank (and thus the SRBs) at some point before landing - can't deploy the landing gear with the tank in the way - but that could possibly be the "MECO" point as I expect that the relative lack of aerodynamics and lifting surface mean that they wouldn't make it back to land even if the orbiter could.
On the other hand, the OMS seems like a much more conventional choice. It's underpowered compared to the SSMEs or SRBs, but with the external tank and SRBs jettisoned, and the orbiter flying on aerodynamic control, it wouldn't surprise me that much if the OMS has enough power to get the orbiter home. They're fueled from an internal tank (they're mainly used in orbit, when the external tank has already been jettisoned), and actually carry quite a bit of fuel. They are throttlable, steerable, and restartable. I'm pretty sure their nozzle expansion isn't too great for sea-level use. Finally, the orbiter is clearly designed for powered maneuvers under OMS alone (can't use the main engines in orbit once the external tank separates), unlike the SRBs.