An English acquaintance used to sing only the standard single verse, but she added a chorus that somehow included repetitions of "How's your father?" Wish I knew where she was these days; I'd ask for more!
I had an Irish friend who'd follow the canary ditty with a segue to:
"Green grow the rushes-o,
Blackbirds and thrushes-o,
If ever you pish into the wind
You're sure to wet your britches-o."
I guess the connection was birds.