We extend our formulation of the covariant quantum superstring as a WZNW model with N = 2 superconformal symmetry to N = 4. The two anticommuting BRST charges in the N = 4 multiplet of charges are the usual BRST charge QS and a charge QV proposed by Dijkgraaf, Verlinde and Verlinde for topological models. Using our recent work on ”gauging cosets”, we then construct a further charge QC which ant...