I think there's an episode of The Muppet Show where Gonzo is panicking that his Mexican Jumping Beans were gone and Animal walks in the background hicuping and jumping, and then Gonzo is chasing Animal as Animal laughs and has a good time running. That's the only time I've seen them interact. It's funny how there's some characters that rarely interact with each other. I can understand if it's characters that are performed by the same Muppeteer but sometimes there's rare scenes for example I think there was an episode where Miss Piggy karate chops Fozzie or chases after him, I don't remember which episode it was. I think it was from Season 2. I remember there was the episode where Dr. Teeth sings "Jack the Knife" and Sam tries to put a stop to it and Dr. Teeth explains the so called violent song is really about Jack going off to buy his wife sofa pillows. One of my favorite bits.
Anyway, I wonder myself which characters rarely ever interacted with each other. Ususally it's characters performed by the same Muppeteer. But characters that aren't like Gonzo and Animal, yeah it's interesting to think about.