We "sang" a version of this in my very Jewish Washington Heights (NYC) neighborhood pre-1948 (we would not have said "Palestine" after the establishment of the State of Israel). Our last verse was:

Men of circumcision,
Join the 44th Division,
And fight, fight, fight for Palestine!

Another favorite was one Philip Roth sometimes receives credit for, since he quoted it in "Portney's Complaint" as a cheer used by his New Jersey high school. We'd chant our version of that one:

Izzy, Abie, Jakey, Sam.
We are the boys who eat no ham.
Can you guess our favorite dish?
Matzos and gefilte fish.

We play baseball, hockey, soccer.
We keep matzos in our locker.

I think there were two more lines. Anyone remember them?