  We propose a scheme of multipartite entanglement distillation driven by a
complementary pair of stabilizer measurements, to distill directly a wider
range of states beyond the stabilizer code states (such as the
Greenberger-Horne-Zeilinger states). We make our idea explicit by constructing
a recurrence protocol for the 3-qubit W state. Noisy W states resulting from
typical decoherence can be directly purified in a few steps, if their initial
fidelity is larger than a threshold. For general input mixed states, we observe
distillations to hierarchical fixed points, i.e., not only to the W state but
also to the 2-qubit Bell pair, depending on their initial entanglement.
