user-1: What is the highest number of pieces from one side that can be involved in a checkmate? "Involved in a checkmate" is defined below.
A non-king piece is involved in a checkmate 'if removing it from the checkmate position would change the position to one which is either not checkmate or is illegal'.  The king is involved in a checkmate if it is the only piece of the checkmating side that attacks one of the other king's escape squares.

user10380: Here's another way to involve all 16 White units. This time the check is orthogonal.
[Title "All 16 White units in the mating-net"]
[fen "r2N1R2/1p2pn2/PBB1P3/Q4kPP/8/5nPK/PNPP1R2/q1r1b3 w - - 0 1"]
[StartFlipped "0"]

1.

wNd8 stops Ke6; wPg5, Kf6; wPh5, Kg6; wBc6, Ke4; wPg3, Kf4; wK, Kg4;
wRf8, N7e5;
wPa6, Rxa5; wBb6, b5; wPe6, e5;
wPa2, Qxa5; wNb2, Qe5; wPc2, Rc5; wPd2, Bxa5; wRf2, N3e5.
Legality: Perhaps wPa6 did bxPa and wPg5 did fxPg. (Or perhaps one of them captured [bBc8].)

user12629: My original thought was that the limit was nine pieces; one for each of the 8 squares the king can run to, plus one for check:
8/2K5/8/3Pk3/2P2PPB/3P2P1/2N5/8 w - - 0 1

But as someone mentioned in a comment, pieces can become "necessary" even if they aren't controlling one of those squares.  If the black pieces don't have to be "necessary", then we can have a board where ALL the white pieces are "necessary" to make this be a legal checkmate, although seven of them are just preventing a check.
The rest do the actual job of checkmate.
3b1q1q/1N2PRQ1/rR3KBr/B4PP1/2Pk1r1b/1P2P1N1/2P2P2/8 b - - 0 1


user14079: Here is a solution with all 16 white pieces, all mandatory for checkmate, without promoted units and without needing to protect the white king from checks. If you remove any white piece but the king, the position is still legal but not a checkmate anymore. Moving the wK to a random square (say, h1) would also destroy the mate.
QNr1R1b1/P1BpnP2/3P4/qP4Pr/Rn2kP2/1N4PB/2P2K2/8 w - - 0 1

Last move is Nc6-b8# or d5-d6#.

-1: <p>What is the highest number of pieces from one side that can be involved in a checkmate? &quot;Involved in a checkmate&quot; is defined below.</p>
<p>A non-king piece is involved in a checkmate 'if removing it from the checkmate position would change the position to one which is either not checkmate or is illegal'.  The king is involved in a checkmate if it is the only piece of the checkmating side that attacks one of the other king's escape squares.</p>
 10380: <p>Here's another way to involve all 16 White units. This time the check is orthogonal.</p>
<pre><code>[Title &quot;All 16 White units in the mating-net&quot;]
[fen &quot;r2N1R2/1p2pn2/PBB1P3/Q4kPP/8/5nPK/PNPP1R2/q1r1b3 w - - 0 1&quot;]
[StartFlipped &quot;0&quot;]

1.
</code></pre>
<p>wNd8 stops Ke6; wPg5, Kf6; wPh5, Kg6; wBc6, Ke4; wPg3, Kf4; wK, Kg4;
wRf8, N7e5;
wPa6, Rxa5; wBb6, b5; wPe6, e5;
wPa2, Qxa5; wNb2, Qe5; wPc2, Rc5; wPd2, Bxa5; wRf2, N3e5.</p>
<p>Legality: Perhaps wPa6 did bxPa and wPg5 did fxPg. (Or perhaps one of them captured [bBc8].)</p>
 12629: <p>My original thought was that the limit was nine pieces; one for each of the 8 squares the king can run to, plus one for check:</p>

<pre><code>8/2K5/8/3Pk3/2P2PPB/3P2P1/2N5/8 w - - 0 1
</code></pre>

<p>But as someone mentioned in a comment, pieces can become "necessary" even if they aren't controlling one of those squares.  If the black pieces don't have to be "necessary", then we can have a board where ALL the white pieces are "necessary" to make this be a legal checkmate, although seven of them are just preventing a check.
The rest do the actual job of checkmate.</p>

<pre><code>3b1q1q/1N2PRQ1/rR3KBr/B4PP1/2Pk1r1b/1P2P1N1/2P2P2/8 b - - 0 1
</code></pre>
 14079: <p>Here is a solution with all 16 white pieces, all mandatory for checkmate, without promoted units and without needing to protect the white king from checks. If you remove any white piece but the king, the position is still legal but not a checkmate anymore. Moving the wK to a random square (say, h1) would also destroy the mate.</p>

<pre><code>QNr1R1b1/P1BpnP2/3P4/qP4Pr/Rn2kP2/1N4PB/2P2K2/8 w - - 0 1
</code></pre>

<p>Last move is Nc6-b8# or d5-d6#.</p>
