One-up-manship rhymes with:
manship, manship, bipartisanship, blankenship, brinkmanship, brinksmanship, chairmanship, championship, citizenship, companionship, craftsmanship, draftsmanship, gamesmanship, gunship, internship, kinship, manship, one-upmanship, partisanship, relationship, salesmanship, showmanship, sportsmanship, statesmanship, upmanship, winship, workmanship