We demonstrate that in addition to the usual fourth-rank superfield ( Wabcd) which describes the on-shell theory, a spinor superfield ( Jα) can be introduced into the 11D geometrical tensors with engineering dimensions less or equal to one in such a way to satisfy the Bianchi identities in superspace. The components arising from Jα are identified as some of the auxiliary fields required for a full off-shell formulation. Our result indicates that eleven-dimensional supergravity does not have to be completely on-shell. The κ-symmetry of the supermembrane action in the presence of our partial off-shell supergravity background is also confirmed. Our modifications to eleven-dimensional supergravity theory are thus likely relevant for M-theory. We suggest our proposal as a significant systematic off-shell generalization of eleven-dimensional supergrravity theory.