  The framework of exceptional field theory is extended by introducing
consistent deformations of its generalised Lie derivative. For the first time,
massive type IIA supergravity is reproduced geometrically as a solution of the
section constraint. This provides a unified description of all ten- and
eleven-dimensional maximal supergravities. The action of the E7 deformed theory
is constructed, and reduces to those of exceptional field theory and gauged
maximal supergravity in respective limits. The relation of this new framework
to other approaches for generating the Romans mass non-geometrically is
discussed.
