The hidden on-shell E(7(7)) symmetry of maximal supergravity is usually discussed in a truncation from D=11 to four dimensions. In my talk, I will reverse this logic and start from a theory with manifest off-shell E(7(7)) symmetry inspired by West's coset construction. I will start with a short motivation of the generalized coset dynamics by explaining the procedure of symmetry enhancement for the familiar example of general relativity. Maximal supergravity will then be related to an extension of this procedure, whose dynamics takes place in a 4+56 dimensional exceptional geometry, following de Wit and Nicolai. Requiring a bosonic symmetry enhancement will be shown to uniquely fix the couplings in the Lagrangian as well as potential supersymmetry variations for the 56 dimensional subsector. Truncating this theory to seven dimensions exactly coincides with the truncation of both the dynamics and the supersymmetry variations of D=11supergravity in a truncation to d=7 and in the restriction to the bosonic fields contained in the Cremmer-Julia coset E(7(7))/SU(8).