As the subject suggests, there's always been this idea lurking in my mind and I'm pretty sure other people had thought about it too. Being the beginner player I was way back, I would buy companions on the wrong character or just on one singular character that may ever use the companion in question again. I would think some other players would understand this.

I've been eyeing Doctor Noh on my Buccaneer for awhile now and I've been wanting it on my Witchdoctor...

Vanessa Mythdust on Jul 22, 2017 wrote:

While I agree it would be nice, a potential problem I see with this is overleveled companions. Meaning, you could level a companion on a max level pirate and then trade it to a brand new character. Unless the companion resets following a trade, you'd have a very overpowered companion (in addition to exceeding your pirate's level).

As that is true, I was thinking that it would have limitations that I forgot to include.
Like you cannot have companions above your level (Unless your max bc I know level 71 or 72 companions exist) and can only trade companions to characters that are under or exactly the Companion's level.