We develop an exceptional generalised geometry formalism for massive type IIA supergravity. In particular, we construct a deformation of the generalised Lie derivative, which generates the type IIA gauge transformations as modified by the Romans mass. We apply this new framework to consistent Kaluza-Klein reductions preserving maximal supersymmetry. We find a generalised parallelisation of the exceptional tangent bundle on S6, and from this reproduce the consistent truncation ansatz and embedding tensor leading to dyonically gauged ISO(7) supergravity in four dimensions. We also discuss closely related hyperboloid reductions, yielding a dyonic ISO(p, 7 − p) gauging. Finally, while for vanishing Romans mass we find a generalised parallelisation on Sd, d = 4, 3, 2, leading to a maximally supersymmetric reduction with gauge group SO(d + 1) (or larger), we provide evidence that an analogous reduction does not exist in the massive theory.