When I was in the service this was sometimes used as a marching song, usually with a call-response format and -- as far as I know -- verses being made up on the spot. It could get pretty ribald at times.
I had also heard it as a kids' "dirty" song that wasn't to be sung around adults for fear of a thick ear. A couple of the verses from those days are:
The first marine went over the fence, parley-vous
The second marine ....
The third marine went over the fence and milked a cow with a monkey wrench.
Hinky-dinky parley-vous
The first marine whittled the bean...
The second marine cooked the bean....
The third marine he ate the bean
And blew a hole in the submarine
Hinky-dinky .....
That's all I can remember. Maybe it's better that way....
cheers, ddw