Stereophonics
Muse supported Stereophonics a "couple" of times in the USA.[1] Matthew Bellamy indicated that he found it pleasant to socialise with them between these gigs.[1] Due to a misunderstanding between each band's agents, sometime during the Origin of Symmetry tour the Stereophonics made false claims about the band to the press, claiming that Muse had turned down a twenty thousand pound concert offer because they wanted more money.[1] Booking agents apparently referenced these allegations when Muse were booking concerts.[1]
Bellamy alleged that the Stereophonics asked for 1.7 million pounds to perform at the Carling Weekend, Reading and that they'd taken the Performing Rights Society money from a band that supported them.[1]
Stereophonics also played the main stage at V Festival 2008, before Muse's headlining slot
There are no indications that either the Stereophonics or Muse are musically influenced by the other.