Could a player sacrifice 3 of his pieces , the opponent's King being forced to take each piece in a sequence of moves where the opponent's King lands on a space where it is promptly checkmated? A kind of 3-move forced checkmate. Could this be done with 4 moves?
On a similar note, here is a pretty problem forces Black to take all 8 pieces and a pawn in order to give checkmate with the last pawn!
[Title "Johann Christoffel Van Gool, Le Journal de Genève 1979"] [FEN "2n1QN2/2Np1pk1/1b1p1p2/1Kp1B1p1/1R3p2/2P1r3/1r1nPRb1/1B5q w - - 0 1"] 1. Nfe6+ dxe6 2. Nxe6+ fxe6 3. Bxf6+ Kxf6 4. Rxf4+ gxf4 5. Qf8+ Ke5 6. Qxf4+ Kd5 7. Qg5+ Re5 8. e4+ Bxe4 9. Qxd2+ Rxd2 10. Ba2+ Rxa2 11. Rd4+ cxd4 12. c4#
Additionally, I found another problem in a Dutch article by Tim Krabbe where White gives away four queens, two rooks, and two knights to also give mate with the last pawn. The most heaviest bag of material sacrificed in a chess problem ever!
[Title "Mate in 13 Moves, Gerhad Josten, Tim Krabbe “ONSTERFELIJKE WOESTHEID”, 2000"] [FEN "1q4r1/1bp2pQ1/3Q4/1Kp1pr2/1n1pkp1p/RQ1RN3/nbnP4/QN6 w - - 0 1"] 1. Kc4 cxd6 2. Nc3+ Nxc3 3. Qh1+ f3 4. Qxh4+ Rf4 5. Qhh7+ f5 6. Qxb7+ Qxb7 7. Qxb7+ d5+ 8. Qxd5+ Ncxd5 9. Nxd5 Nxd5 10. Re3+ Ncxe3+ 11. Qxe3+ Nxe3+ 12. Rxe3+ dxe3 13. d3#