Towards SO(2,10)-invariant M-theory: Multi-Lagrangian fields

The SO(2, 10) covariant extension of M-theory superalgebra is considered, w ith the aim to construct a correspondingly generalized M-theory, or 11-D su pergravity. For the orbit corresponding to the 11-D supergravity multiplet, the simplest unitary representations of the bosonic Dart of this algebra, with sixth-rank tensor excluded, are constructed on a language of field the ory in 66-D space-time. The main peculiarities are the presence of more tha n one equation of motion and the corresponding Lagrangians for a given fiel d and that the gauge and SUSY invariances of the theory mean that the sum o f variations of these Lagrangians (with different variations of the same fi eld) is equal to zero.