  We construct an infinite system of non-linear duality equations, including
fermions, that are invariant under global E11 and gauge invariant under
generalised diffeomorphisms upon the imposition of a suitable section
constraint. We use finite-dimensional fermionic representations of the
R-symmetry E11 to describe the fermionic contributions to the duality
equations. These duality equations reduce to the known equations of E8
exceptional field theory or eleven-dimensional supergravity for appropriate
(partial) solutions of the section constraint. Of key importance in the
construction is an indecomposable representation of E11 that entails extra
non-dynamical fields beyond those predicted by E11 alone, generalising the
known constrained p-forms of exceptional field theories. The construction
hinges on the tensor hierarchy algebra extension of E11, both for the bosonic
theory and its supersymmetric extension.
