Childrens book - Elephant who wanted to look different

I'm trying to find the name of a book I had as a child in the 70's. All I can remember was that it was about an elephant who met different animals and was jealous of the different things they had - so he somehow grew different parts of them - like getting butterfly wings. By the end he couldn't recognise himself and so realised that he was fine just as he was originally.
Does this ring a bell with anyone?
Thank you

Absolutely, it does! I've got copy of it in the bookcase of as-yet-uncataloged children's books. Unfortunately, it's buried behind a ton of things that belong to my youngest son, who is back living with us temporarily. And, I can't remember the name of it, although I know I read it to my kids at least a dozen times. I'm sure it'll come to me around 3 a.m.

Not "The Saggy Baggy Elephant" is it?

It also reminds me of "I Wish That I Had Duck Feet" by Theo LeSig and B. Tobey,:

A young boy weighs the pros and cons of possessing various animal appendages—such as a duck's feet, a deer's antlers, a whale's spout, an elephant's trunk, and a long, long tail—only to decide that he's better off just being himself.

The Whingdingdilly has the same theme, but is about a dog instead of an elephant. It'sone of the few books from my childhood I've kept and still enjoy.

The Mixed Up Chameleon by Eric Carle sounds pretty similar. It is about a Chameleon, but he does end up with elephant parts at one point.

Is it Lord Rex, the Lion Who Wished by David McKee? The description on Google Books is "A lion, longing for the features of various animals, has all his wishes granted and becomes a ridiculous-looking animal."

Thank you so much - it's Lord Rex - that was an amazing bit of memory / detective work. I shall now go and buy a copy for my baby niece who I'm sure will enjoy it as much as I did. Thank you

Yay, so glad I could help! :) Google Books is an amazing thing.