Indeed, there are many possible [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 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: Journal Entry #267
Additionally, I know of this 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 CSE question by the user @Peter, in which both sides are forced to let the other mate them!