The multi-party maximal-entanglement definition used in the paper is "no matter how you cut it into two pieces, the two pieces are maximally entangled". Monogam

The multi-party maximal-entanglement definition used in the paper is "no matter how you cut it into two pieces, the two pieces are maximally entangled". Monogamy isn't an obstacle because the definition is always using two pieces. A 3-qubit state with this property is the |000> + |111> state. But |0000> + |1111> doesn't work as a 4-qubit state because when you cut it into evenly sized pieces you should be able to distill 2 bell pairs instead of 1.