Indeed, there are [many](https://chess.stackexchange.com/questions/24061/what-is-the-highest-number-of-possible-forced-checkmates-in-a-legal-position) [possible](https://chess.stackexchange.com/questions/24033/a-position-in-which-checkmate-is-forced-obligatory/24034#24034) [positions](https://puzzling.stackexchange.com/questions/30409/highest-number-of-mates/87225#87225) in which all mates are forced on the first ply. Since you ask not for that, I shall provide examples with more than one move by both sides.

Here is the known, and overall, length record for both sides having multiple legal moves since you said that a single line "isn't too satisfying."

    [Title "Alexey Khanyan, Tim Krabbe's Website Diary Entry #267 2008, Mate In 11 Moves/22 Plies"]
    [FEN "4Q2Q/4r3/4n1n1/1bbK1krn/RR1RR1RR/2qn1R1n/4n1nN/Q3Q3 b - - 0 1"]
    [startflipped ""]

    1... Ng2f4+ 2. Rfxf4+ N2xf4+ 3. Rgxf4+ Nh3xf4+ 4. Rhxf4+ Ndxf4+ 5. Rxf4+ Nhxf4+ 6. Rxf4+ Ngxf4+ 7. Rxf4+ Nxf4+ 8. Rxf4+ Kxf4+ 9. Qee5+ Qxe5+ 10. Qaxe5+ Rgxe5+ 11. Qxe5+ Rxe5+ 12. Qxe5#

Source: [Diary Entry #267](https://timkr.home.xs4all.nl/chess2/diary_14.htm)

Additionally, I know of [this](https://pdb.dieschwalbe.de/P1108329) simple problem that illustrates it with either playing giving mate.

    [Title "Eugene B. Cook, The Chess Amateur 1926, Mate In For White And Black"]
    [FEN "Bk6/1P6/1P3p2/8/8/2P3p1/6p1/6Kb w - - 0 1"]

Lastly, be sure to check out a funny mutual zugzwang position in [this](https://chess.stackexchange.com/questions/9062/full-board-with-full-point-mutual-zugzwang) CSE question by the user @Peter, in which both sides are forced to let the other mate them!