Elmyra has had an odd career, being both a supporting character on Tiny Toons and Animaniacs, and a title character on Pinky and The Brain and Elmyra and her own show that I can't remember the name of.( I can't remember which came first)
Elmyra's first continual pet was Furrball (the Tiny Toons equivalent of Sylvester who also had a few shorts to himself) She eventually gained a dog while on Animanics. The dog looked like an overgrown Shih Tzu, with no legs and just a nose, who made little muffled woofing noises at things. And of course for some reason the scientists at Acme Labs needed some cash, so they sold her Pinky and The Brain.
While on Tiny Toons she spent her time chasing anything that was cute and adorable, then caging it, and subjecting it to the most heinous cuddly torture ever conceived by man.
When she moved to Animaniacs, her character at first was only there to introduce the Skullhead Bonyhands shorts, by pulling the skull hair barrette out of her hair, and singing, "It's the Mr Skullhead Show, Starring him: Mr Skullhead, 'Cause it's his show that he has, Mr Skullhead!" in that odd gooey voice of hers. Later she got to become a regular and chase The Warners around, and had a few shorts.
When she got her own show, which was very short lived, I only saw two or three episodes, It featured her entire family and much less in the way of pets. Her family consisted of several characters who's names I can't remember (someone please tell me!) Her father was an inventor, and mother was a realtor. There was the obligatory, angry at the world, punk teenaged sister, the younger brother who thought that he was a super hero, and the baby brother, who, if lost his pacifier let out an earth shattering wail, that could only be stopped by replacing said pacifier (I also think he had super human strength for some reason that wasn't explained). The show was fun, even though it didn't really have the room to get off. The family characters worked well together. Elmyra was the main character of every episode, if not the one committing the action that furthered the story.
And then there was Pinky and The Brain and Elmyra. I don't know why this show was made. I thought Pinky and The Brain was perfect how it was, but it was interesting that The Brain had found a sidekick stupider than Pinky, albeit not as entertaining.