Is there a double-forced mate position? A usual forced mate position is where the winning player can play in a way that ensures checkmate, no matter what (legal) moves the opponent makes (unless the game ends due to a non-play reason, i.e. resignation, draw accepted, time ran out.)
What I'm asking about here is what I'll call a double-forced mate:  A position where checkmate is ensured no matter what (legal) moves either player makes.
With this rule alone we can find a position such as this, where white has only one legal move, resulting in checkmate.  Let's call this type 1.
Type 1:
[FEN &quot;K1k5/1q6/P7/B3N3/8/8/8/8 w - - 0 1&quot;]

1. axb7#

The only option is axb7#. However, this isn't too satisfying as a &quot;double&quot; forced mate, as there was only a single possible move to continue.  We can explore positions that have multiple possibilities, but still ensure checkmate absolutely.
Type 2:
[FEN &quot;k7/2QQQQQQ/KQ1QQQQQ/QQQ1QQQQ/QQQQ1QQQ/QQQQQ1QQ/QQQQQQ1Q/QQQQQQQ1 w - - 0 1&quot;]

White has many legal moves, but every one of them results in an immediate checkmate.  Still, I feel this question isn't quite answered, as in a true double-forced checkmate, both players should play a role. (Also, this position clearly isn't possible from a standard board start. And even if it were, it doesn't seem that it could be achieved without first creating a stalemate.)  Let's finally look to type 3.
Type 3:
The true double-forced mate: A position where checkmate is ensured no matter what (legal) moves either player makes, however there is at least some line where both players make a move. Meaning not every legal ply in the start position is an immediate checkmating move.
Do you know of (or can you find) any such chess positions of (type 3) double-forced mate?  Or can you prove that this is not possible?
Also, share if you have any interesting or more plausible examples of type 1 and 2.
Indeed, there are many possible positions 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 &quot;isn't too satisfying.&quot;
[Title &quot;Alexey Khanyan, Tim Krabbe's Website Diary Entry #267 2008, Mate In 11 Moves/22 Plies&quot;]
[FEN &quot;4Q2Q/4r3/4n1n1/1bbK1krn/RR1RR1RR/2qn1R1n/4n1nN/Q3Q3 b - - 0 1&quot;]
[startflipped &quot;&quot;]

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
Additionally, I know of this simple problem that illustrates it with either playing giving mate.
[Title &quot;Eugene B. Cook, The Chess Amateur 1926, Mate In For White And Black&quot;]
[FEN &quot;Bk6/1P6/1P3p2/8/8/2P3p1/6p1/6Kb w - - 0 1&quot;]

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!