ABSTRACT Rotation and mass-loss are crucially interlinked properties of massive stars, strongly affecting their evolution and ultimate fate. Massive stars rotating near their break-up limit shed mass centrifugally, creating Be stars with circumstellar discs and possibly driving outbursts. Using the mesa stellar evolution code, we examine the effects of efficient angular momentum transport on the main-sequence and post-main-sequence rotational evolution of massive stars. In rapid rotators, angular momentum transported from the contracting core to the expanding envelope can spin-up the surface layers past the break-up rate, particularly for stars near (or beyond) the end of the main-sequence and in low-metallicity environments. We also demonstrate that centrifugal instabilities could arise in rapidly rotating massive stars, potentially triggering the S Doradus outbursts observed in luminous blue variable stars. Prior mass accretion from a binary companion increases both the likelihood and the intensity of centrifugal mass-loss. We discuss implications for massive stellar evolution, Be stars, and luminous blue variables.