"pummel" is OK but a bit narrow to be close to the top of the list. "vaccine" is too narrow.
We wouldn't usually have xrefs to the components of a 複合動詞.

@@ -20,3 +19,0 @@
-<xref type="see" seq="1408810">打つ・1</xref>
-<xref type="see" seq="1408810">打つ・5</xref>
-<xref type="see" seq="1257800">捲る・まくる・2</xref>
@@ -24 +20,0 @@
-<gloss>to pummel</gloss>
@@ -29 +25 @@
-<gloss>to give vaccine after vaccine</gloss>
+<gloss>to pummel</gloss>

https://dictionary.cambridge.org/dictionary/english/pummel
to hit someone or something repeatedly, especially with your fists (= closed hands):
The boxer had pummelled his opponent into submission by the end of the fourth round.

https://www.collinsdictionary.com/dictionary/english/pummel
REGIONAL NOTE:  
in AM, use pummeling, pummeled
VERB
If you pummel someone or something, you hit them many times using your fists.
He trapped Conn in a corner and pummeled him ferociously for thirty seconds. [VERB noun] 

https://www.merriam-webster.com/dictionary/pummel
pummel
verb
pum·​mel ˈpə-məl 
: POUND, BEAT

I came here to suggest "pummel" (below).  Then I googled and saw a bunch of baseball players, and realized that "belt hit after hit" was probably a baseball reference, then I saw this vaccine thing and got incredibly confused:

「ワクチンを打って打って打ちまくるしかない」  2022.1.18  NHK
https://twitter.com/KDystopia/status/1485704549478572032
All googlable.  Not massively common or anything, but easily understandable by a Japanese person. "ワクチン" is also *optional* in context.
"ワクチンを打ちまくる" 
"ワクチンを打って打って打ちまくるしかない" 
"ワクチンを打ちまくれ"

At the end I finally get that 捲る is a generic suffix. 打ちまくる isn't even *in* sankoku, in any form.  But 捲る[2] is. This applies to *all* senses of 打つ. I see we have a bunch if ~捲る entries. Often times we do not gloss entries that are compounds like this.  Obviously it's helpful to provide more nuanced English glosses(like "pummel"), but there is also a certain argument for deleting this term entirely to fall back on 打ち + 捲る glosses, since 打つ has *so many* potential senses.

Otherwise, it seems like the proper thing to do is split this into a bunch of senses...

The problem is that having this entry here, limited to the hitting sense, masks the fact that 打ちまくる just means to 打つ repeatedly, whatever 打つ might mean.  We might be mislead to think the Japanese are aggressively pounding away at vaccines.

================

Entirely limited to "pummel"(I wrote all of this first): Am I crazy?  I feel like we have a word for "to hit repeatedly" and "to belt hit after hit" and "to unleash a barrage of blows".  But I can't find much J->E support for it anywhere.  Should we share this with the world?

I encountered 撃ちまくる, with the other kanji. But even that one could have used "pummel" I think.  Fighter calling on his mage companions to finish off a dragon by blasting it with magic. "今だ。撃ちまくれ！" "Ok, shoot it now!" or "Now! Fire!"

@@ -20,0 +21,2 @@
+<xref type="see" seq="1408810">打つ・5</xref>
+<xref type="see" seq="1257800">捲る・まくる・2</xref>
@@ -22 +24,2 @@
-<gloss>to belt hit after hit</gloss>
+<gloss>to pummel</gloss>
+<gloss>to belt hit after hit (e.g. in baseball)</gloss>
@@ -25,0 +29 @@
+<gloss>to give vaccine after vaccine</gloss>

OK. I'll split it out.

@@ -8,3 +7,0 @@
-</k_ele>
-<k_ele>
-<keb>撃ちまくる</keb>
@@ -29,9 +25,0 @@
-</sense>
-<sense>
-<pos>&v5r;</pos>
-<pos>&vt;</pos>
-<s_inf>esp. 撃ちまくる</s_inf>
-<gloss>to fire (a gun) ceaselessly</gloss>
-<gloss>to fire away</gloss>
-<gloss>to blaze away</gloss>
-<gloss>to fire volley after volley</gloss>

gg5

撃ちまくる is only used for shooting. I think it should be a separate entry.

@@ -23,4 +23,6 @@
-<xref type="see" seq="1408810">打つ・うつ・1</xref>
-<gloss>to pound away</gloss>
-<gloss>to hit at random</gloss>
-<gloss>to hit ceaselessly</gloss>
+<xref type="see" seq="1408810">打つ・1</xref>
+<gloss>to hit repeatedly</gloss>
+<gloss>to belt hit after hit</gloss>
+<gloss>to unleash a barrage of blows</gloss>
+<gloss>to pound away (at a keyboard)</gloss>
+<gloss>to hammer away</gloss>
@@ -31 +32,0 @@
-<xref type="see" seq="1253570">撃つ・うつ</xref>
@@ -33 +34,3 @@
-<gloss>to blaze away (at the enemy)</gloss>
+<gloss>to fire (a gun) ceaselessly</gloss>
+<gloss>to fire away</gloss>
+<gloss>to blaze away</gloss>

Quiet. Closing.