In this paper we present a rank analogue to Stein's two-stage procedure. We analyze its behavior to second order using existing asymptotic expansions for fixed sample size rank tests and recent results on combinations of independent rank statistics.
"Second Order Analysis of Two-Stage Rank Tests for the One-Sample Problem." Ann. Statist. 19 (2) 1042 - 1052, June, 1991. https://doi.org/10.1214/aos/1176348136