The Shuttle did have limited engine out capability. The only in-flight engine-out (as opposed to a pad abort after SSME ignition and before SRB ignition, which happened five times) was STS-51-F with a successful abort to orbit. The various other engine-out contingency modes were never used, but they did exist.
Initially only single engine out was broadly survivable; after the Challenger disaster new abort procedures were developed that made two engines out survivable during all of flight and even all three engines out at some points.
The big caveat here is that most of these modes were never tested, and the risk of failure during the more demanding aborts was substantial. RTLS abort was famously not tested on STS-1 because it was considered riskier than going all the way to orbit on the Shuttle's first crewed flight.
Initially only single engine out was broadly survivable; after the Challenger disaster new abort procedures were developed that made two engines out survivable during all of flight and even all three engines out at some points.
The big caveat here is that most of these modes were never tested, and the risk of failure during the more demanding aborts was substantial. RTLS abort was famously not tested on STS-1 because it was considered riskier than going all the way to orbit on the Shuttle's first crewed flight.