Of course, this also scans to "Mary had a little lamb", allowing verses to flow back and forth between all verses:

Mary had a little lamb,
It's fleece was white as snow
And everywhere that Mary went
The lamb was sure to go.

Mary had a little lamb.
She also had a bear.
I've often seen her little lamb,
But I've never seen her bear.

Mary had a little bear,
She treated it so kind.
And everywhere that Mary went
You'd see her bear behind.

Mary had a little dress,
The skirt was split in half.
And every step that Mary took,
The boys would see her calf.

Mary had another dress,
Split right up the front.
But she didn't wear that one.

Mary had a little pig.
She couldn't stop it gruntin'
She took it down a little path
And kicked its little head in