  We introduce the concept of spinful many-particle Majorana modes with local
odd operator products, thereby preserving their local statistics. We consider a
superconductor-double-quantum-dot system where these modes can arise with
negligible Zeeman splitting when Coulomb interactions are present. We find a
reverse Mott-insulator transition, where the even- and odd-parity bands become
degenerate. Above this transition, Majorana operators move the system between
the odd-parity ground state, associated with elastic cotunneling, and the
even-parity ground state, associated with crossed Andreev reflection. These
Majorana modes are described in terms of one, three, and five operator
products. Parity conservation results in a 4% periodic supercurrent in the even
state and no supercurrent in the odd state.
