user21513: A fun thing to do is to try to achieve specific "achievements" (like these) in real games.
One such achievement is to checkmate with a king move. As the king itself obviously can't deliver checks, it would have to be through a discovery (or castling, but one seldom has castling rights preserved in the endgame).
When can this be forced?
It seems to require more fire power than a regular checkmate
A queen and a heavy piece is enough to force this through the standard knight-opposition manoeuvre to drive the king to a corner and then setting up the checkmate
[title "Queen + heavy piece"]
[fen "8/1K6/5k2/8/8/8/8/R2Q4 w - - 0 1"]

1. Qd5 Kg7 2.Qe6 Kh8 3.Qe7 Kg8 4.Kb8 Kh8 5.Ra8 Kg8 6.Kb7#

Queen and bishop doesn't seem to be enough, at least with the same setup. While the king can cover the g8 prison square while simultaneously uncovering the bishop, the enemy king unfortunately escapes down the h file:
[title "Queen + bishop"]
[fen "7k/4Q2/5K2/8/8/8/8/B7 w - - 0 1"]

1. Kf7+ Kh7

Queen + bishop + light piece to cover h7 would be enough.
Some basic checkmates like KQvK, KRvK and KBNvK are obviously not possible since their required setups have no room for a discovery
What other material combinations can force a king move checkmate?

user11144: I also looked a bit into "king discovered mates that can be forced from any nonspecial position", and the following material suffices:

RR (obvious)
RXY where X and Y are light officers (Ka5 Ra1 Nd7 Nd8, Ka8 is easily forced, Kb6#; replacing a knight with a bishop is analogous)
XYZ also suffices except for 3 N (Kc6 Bh1 Nd7 Nb4, Ka8 is easily forced, Kb6#; Nd7 may be replaced with Bh2)

On the other hand...

QX does not force (neither B or N can cover b8 and c8 together), thus RX neither

Since P can promote and black material must be captured before mate, this should cover all cases (e.g. QXY can be "reduced" to XYZ).

user32606: As you noted, no "K + single piece" can achieve this. Here is an overview to the "K + two x" cases, of which only three cases don't work.
Note that these base cases allow for any further pieces, so there are only 8 exceptions that can't achieve this.
Queen+x works in all cases
1. KQPvK
[fen "7k/5P2/7K/7Q/8/8/8/8 w - - 1 0"]

1. Kg6

2. KQBvK
[fen "7k/5B2/7K/7Q/8/8/8/8 w - - 1 0"]

1. Kg6

3. KQNvK
[fen "7k/4N3/7K/7Q/8/8/8/8 w - - 1 0"]

1. Kg6

4. KQRvK
[fen "RK5k/3Q4/8/8/8/8/8/8 w - - 1 0"]

1. Kb7

5. KQQvK
[fen "7k/5Q2/7K/7Q/8/8/8/8 w - - 1 0"]

1. Kg6

Bishop+x works in all cases
6. KBPvK
[fen "7k/5P2/5K2/4B3/8/8/8/8 w - - 1 0"]

1. Kg6

7. KBNvK
[fen "7k/4N3/5K2/4B3/8/8/8/8 w - - 1 0"]

1. Kg6

8. KBBvK
[fen "7k/5B2/5K2/4B3/8/8/8/8 w - - 1 0"]

1. Kg6

9. KBRvK
[fen "R3K2k/8/6B1/8/8/8/8/8 w - - 1 0"]

1. Kf7

Rook+xworks in all cases
10. KRPvK
[fen "R3K2k/8/6P1/8/8/8/8/8 w - - 1 0"]

1. Kf7

11. KRNvK
[fen "R3K2k/8/5N2/8/8/8/8/8 w - - 1 0"]

1. Kf7

12. KRRvK
[fen "RK5k/2R5/8/8/8/8/8/8 w - - 1 0"]

1. Kb7

KRBvK, KRQvK see above.
The 8 exceptions
KPvK, KNvK, KBvK, KRvK, KQvK,
KNNvK, KNPvK, KPPvK

21513: <p>A fun thing to do is to try to achieve specific &quot;achievements&quot; (like <a href="https://rosen-score.vercel.app/" rel="nofollow noreferrer">these</a>) in real games.</p>
<p>One such achievement is to <strong>checkmate with a king move</strong>. As the king itself obviously can't deliver checks, it would have to be through a discovery (or castling, but one seldom has castling rights preserved in the endgame).</p>
<p><strong>When can this be forced?</strong>
It seems to require more fire power than a regular checkmate</p>
<p>A queen and a heavy piece is enough to force this through the standard knight-opposition manoeuvre to drive the king to a corner and then setting up the checkmate</p>
<pre><code>[title &quot;Queen + heavy piece&quot;]
[fen &quot;8/1K6/5k2/8/8/8/8/R2Q4 w - - 0 1&quot;]

1. Qd5 Kg7 2.Qe6 Kh8 3.Qe7 Kg8 4.Kb8 Kh8 5.Ra8 Kg8 6.Kb7#
</code></pre>
<p>Queen and bishop doesn't seem to be enough, at least with the same setup. While the king can cover the g8 prison square while simultaneously uncovering the bishop, the enemy king unfortunately escapes down the h file:</p>
<pre><code>[title &quot;Queen + bishop&quot;]
[fen &quot;7k/4Q2/5K2/8/8/8/8/B7 w - - 0 1&quot;]

1. Kf7+ Kh7
</code></pre>
<p>Queen + bishop + light piece to cover h7 would be enough.</p>
<p>Some basic checkmates like KQvK, KRvK and KBNvK are obviously <em>not</em> possible since their required setups have no room for a discovery</p>
<p><strong>What other material combinations can force a king move checkmate?</strong></p>
 11144: <p>I also looked a bit into &quot;king discovered mates that can be forced from any nonspecial position&quot;, and the following material suffices:</p>
<ul>
<li>RR (obvious)</li>
<li>RXY where X and Y are light officers (Ka5 Ra1 Nd7 Nd8, Ka8 is easily forced, Kb6#; replacing a knight with a bishop is analogous)</li>
<li>XYZ also suffices except for 3 N (Kc6 Bh1 Nd7 Nb4, Ka8 is easily forced, Kb6#; Nd7 may be replaced with Bh2)</li>
</ul>
<p>On the other hand...</p>
<ul>
<li>QX does not force (neither B or N can cover b8 and c8 together), thus RX neither</li>
</ul>
<p>Since P can promote and black material must be captured before mate, this should cover all cases (e.g. QXY can be &quot;reduced&quot; to XYZ).</p>
 32606: <p>As you noted, no &quot;K + single piece&quot; can achieve this. Here is an overview to the &quot;K + two x&quot; cases, of which only three cases don't work.
Note that these base cases allow for any further pieces, so there are only 8 exceptions that can't achieve this.</p>
<h1>Queen+x works in all cases</h1>
<p><strong>1. KQPvK</strong></p>
<pre><code>[fen &quot;7k/5P2/7K/7Q/8/8/8/8 w - - 1 0&quot;]

1. Kg6
</code></pre>
<p><strong>2. KQBvK</strong></p>
<pre><code>[fen &quot;7k/5B2/7K/7Q/8/8/8/8 w - - 1 0&quot;]

1. Kg6
</code></pre>
<p><strong>3. KQNvK</strong></p>
<pre><code>[fen &quot;7k/4N3/7K/7Q/8/8/8/8 w - - 1 0&quot;]

1. Kg6
</code></pre>
<p><strong>4. KQRvK</strong></p>
<pre><code>[fen &quot;RK5k/3Q4/8/8/8/8/8/8 w - - 1 0&quot;]

1. Kb7
</code></pre>
<p><strong>5. KQQvK</strong></p>
<pre><code>[fen &quot;7k/5Q2/7K/7Q/8/8/8/8 w - - 1 0&quot;]

1. Kg6
</code></pre>
<h1>Bishop+x works in all cases</h1>
<p><strong>6. KBPvK</strong></p>
<pre><code>[fen &quot;7k/5P2/5K2/4B3/8/8/8/8 w - - 1 0&quot;]

1. Kg6
</code></pre>
<p><strong>7. KBNvK</strong></p>
<pre><code>[fen &quot;7k/4N3/5K2/4B3/8/8/8/8 w - - 1 0&quot;]

1. Kg6
</code></pre>
<p><strong>8. KBBvK</strong></p>
<pre><code>[fen &quot;7k/5B2/5K2/4B3/8/8/8/8 w - - 1 0&quot;]

1. Kg6
</code></pre>
<p><strong>9. KBRvK</strong></p>
<pre><code>[fen &quot;R3K2k/8/6B1/8/8/8/8/8 w - - 1 0&quot;]

1. Kf7
</code></pre>
<h1>Rook+xworks in all cases</h1>
<p><strong>10. KRPvK</strong></p>
<pre><code>[fen &quot;R3K2k/8/6P1/8/8/8/8/8 w - - 1 0&quot;]

1. Kf7
</code></pre>
<p><strong>11. KRNvK</strong></p>
<pre><code>[fen &quot;R3K2k/8/5N2/8/8/8/8/8 w - - 1 0&quot;]

1. Kf7
</code></pre>
<p><strong>12. KRRvK</strong></p>
<pre><code>[fen &quot;RK5k/2R5/8/8/8/8/8/8 w - - 1 0&quot;]

1. Kb7
</code></pre>
<p><strong>KRBvK, KRQvK</strong> see above.</p>
<h1>The 8 exceptions</h1>
<p><strong>KPvK, KNvK, KBvK, KRvK, KQvK</strong>,</p>
<p><strong>KNNvK, KNPvK, KPPvK</strong></p>
