Your favourite band's favourite band

What are some examples of this over the years? The Band? Little Feat? NRBQ? Some non-rootsy possible examples too please.

And what is a true 'your favourite's band favourite band'? Possible criteria (or not): low sales, music is hard to find, they get on especially well with musicians/jam with them, they get recommended to the 'favourite band' by other famous people, regularly brought up interviews but it isn't enough to inspire you to search them out, the singer/guitarist (if either exists) at some point makes a guest appearance on favourite band's album/live show.

Fuck, meant to put this in ILM. Politely ignore :)