I searched PDB for selfstalemate problems, and the only one I found where Black has more material is:
[Title "Ivan Bryukhanov. Problemkiste Apr 2002, 5630. P1016527. b) s=3"]
[fen "1k6/R1R5/nKp5/8/q7/8/8/8 w - - 0 1"]
[StartFlipped "0"]
1.Ra8+ Kxa8 2. Ra7+ Kb8 3. Ra8+ Kxa8=
The OP asks for the materially superior side to have the move, so take the situation after White's played the key move. Now bPc6 is needless. (Bryukhanov needed bPc6 because, without it, 1 Rb7+ win.)
[Title "Ivan Bryukhanov (version)"]
[fen "Rk6/2R5/nK6/8/q7/8/8/8 b - - 0 1"]
[StartFlipped "0"]
1... Kxa8 2. Ra7+ Kb8 3. Ra8+ Kxa8=
Black's pieces trap wK. White's rooks give sacrificial checks: Black has no option but to capture White's rooks and leave White with a bare, stalemated king.