user11071: There is a situation that arises occasionally, where each player goes on a rampage through the other player's pieces (often using a queen), never stopping to recapture or defend. It usually ends when either there is no more material to safely capture, or with check.
Is there a term for this kind of war on two fronts?

user26984: It would be an example of repeated Zwischenzugs, where instead of making the expected move (a recapture), each player makes an intermediate move—capturing a different piece.
Zwischenzug is a general expression applying to any intermediate move; I don’t know if there is a more specific term for the scenario you describe.

user21754: I agree with @DavidH, the best technical description is multiple (consecutive) zwischenzugs. As for a more specific term, I don't know an established one either, so maybe it's time to invent one. I propose to call the scenario you describe a caterpillar (line), after the famous picture book by Eric Carle, The Very Hungry Caterpillar. According to Wikipedia:

The book features a very hungry caterpillar who eats his way through a wide variety of foodstuffs before pupating and emerging as a butterfly.

I've used this image in teaching, and it tends to work very well, especially if it's a pawn who does most of the capturing. Here's one of my favorite examples:
[Event "Stuttgart simul"]
[Date "1958"]
[White "Tal, Mihail"]
[Black "NN"]
[Result "1-0"]
[FEN "2r1k2r/1p1bppb1/p2p1np1/q3n1p1/3NP2P/2N1BP2/PPPQB3/1K1R3R w k - 0 15"]
[PlyCount "7"]
[Source "Schach 10/1994, p. 69"]

1. hxg5 Rxh1 2. gxf6! Rxd1+
3. Nxd1! Qxd2 4. fxg7! 1-0

That former h-pawn turned out to be a very hungry caterpillar indeed. Black resigned just when the beautiful butterfly was about to emerge on g8.

user8860: If each of the marauding pieces is itself en prise
during most or all of the sequence, it can be called a desperado;
see for example the Bogolyubov-Schmid game cited in Wikipedia's article on
"Desperado (chess)":
https://en.wikipedia.org/wiki/Desperado_(chess)#Bogolyubov_versus_Schmid

user14079: The late Xavier Parmentier, a very succesful chess teacher, writer, and a leading figure in the French chess community for decades, focused on those lines in his calculation exercices and wrote about them in his book "Les secrets de l'initiative aux échecs" (literally: Secrets of Initiative in Chess), and probably in other works.
He dubbed them "supermarket variations" (les variantes supermarché) : each player grabs what he wants on the shelves without interfering in their opponent's captures.

11071: <p>There is a situation that arises occasionally, where each player goes on a rampage through the other player's pieces (often using a queen), never stopping to recapture or defend. It usually ends when either there is no more material to safely capture, or with check.</p>
<p>Is there a term for this kind of war on two fronts?</p>
 26984: <p>It would be an example of repeated <a href="https://en.m.wikipedia.org/wiki/Zwischenzug" rel="nofollow noreferrer">Zwischenzugs</a>, where instead of making the expected move (a recapture), each player makes an intermediate move—capturing a different piece.</p>
<p>Zwischenzug is a general expression applying to any intermediate move; I don’t know if there is a more specific term for the scenario you describe.</p>
 21754: <p>I agree with @DavidH, the best technical description is <em>multiple (consecutive) zwischenzugs</em>. As for a more specific term, I don't know an established one either, so maybe it's time to invent one. I propose to call the scenario you describe a <strong>caterpillar (line)</strong>, after the famous picture book by Eric Carle, <em>The Very Hungry Caterpillar</em>. According to Wikipedia:</p>
<blockquote>
<p>The book features a very hungry caterpillar who eats his way through a wide variety of foodstuffs before pupating and emerging as a butterfly.</p>
</blockquote>
<p>I've used this image in teaching, and it tends to work very well, especially if it's a pawn who does most of the capturing. Here's one of my favorite examples:</p>
<pre><code>[Event &quot;Stuttgart simul&quot;]
[Date &quot;1958&quot;]
[White &quot;Tal, Mihail&quot;]
[Black &quot;NN&quot;]
[Result &quot;1-0&quot;]
[FEN &quot;2r1k2r/1p1bppb1/p2p1np1/q3n1p1/3NP2P/2N1BP2/PPPQB3/1K1R3R w k - 0 15&quot;]
[PlyCount &quot;7&quot;]
[Source &quot;Schach 10/1994, p. 69&quot;]

1. hxg5 Rxh1 2. gxf6! Rxd1+
3. Nxd1! Qxd2 4. fxg7! 1-0
</code></pre>
<p>That former h-pawn turned out to be a very hungry caterpillar indeed. Black resigned just when the beautiful butterfly was about to emerge on g8.</p>
 8860: <p>If each of the marauding pieces is itself <em>en prise</em>
during most or all of the sequence, it can be called a <strong>desperado</strong>;
see for example the Bogolyubov-Schmid game cited in Wikipedia's article on
&quot;Desperado (chess)&quot;:
<a href="https://en.wikipedia.org/wiki/Desperado_(chess)#Bogolyubov_versus_Schmid" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Desperado_(chess)#Bogolyubov_versus_Schmid</a></p>
 14079: <p>The late <a href="https://fr.wikipedia.org/wiki/Xavier_Parmentier" rel="nofollow noreferrer">Xavier Parmentier</a>, a very succesful chess teacher, writer, and a leading figure in the French chess community for decades, focused on those lines in his calculation exercices and wrote about them in his book &quot;<a href="https://www.variantes.com/generalites-echecs/40440-PARMENTIER-Les-secrets-de-l-initiative-aux-echecs-9782916340616.html" rel="nofollow noreferrer">Les secrets de l'initiative aux échecs</a>&quot; (literally: <em>Secrets of Initiative in Chess</em>), and probably in other works.</p>
<p>He dubbed them <strong>&quot;supermarket variations&quot;</strong> (<em>les variantes supermarché</em>) : each player grabs what he wants on the shelves without interfering in their opponent's captures.</p>
