Consistent reductions from D=11 beyond Sasaki-Einstein

The most general class of warped AdS5×M6w supersymmetric solutions in D=11 supergravity permits a consistent truncation to D=5N=2 minimal gauged supergravity. Here we extend this truncation, for a particular subclass of M6 manifolds, to D=5N=4 gauged supergravity coupled to two vector multiplets. We obtain the reduction ansatz by T-duality of a recently discussed type IIB truncation on a generic Sasaki-Einstein five-fold, which becomes non-trivial in D=11 and displays non-standard features due to the G-structure of the internal M6. Using this truncation, we construct two new classes of warped and unwarped non-supersymmetric AdS5 M-theory backgrounds. We also comment on possible extensions of the reduction ansatz to the general class of M6 geometries.