  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 S^6, 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 S^d, 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.
