O!
Ed Harrigan (lyrics) and Dave Braham (music) followed the original up with "Salvation Army Oh!" in 1882, in the play "The McSorleys," published by Wm. A. Pond, NY. Sheet music at American Memory.
There are four verses.

John Braham published "Army So Grand" in 1874 , G. D. Russell, Boston. Braham wrote the music, W. Cavanagh the words. It starts out-
I'm a gay vivandiere, Yes a gay vivandiere,
and the pet of the Army so grand.

This was the same year as "Regular Army O!" by Harrigan and Dave Braham (relared?)

Looks like there may be all sorts of follow-ups to the original.