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The group – which is made up of former Oasis members Liam Gallagher, Gem Archer, Chris Sharrock and Andy Bell – would have no problem working with the rhythm guitarist, real name Paul Arthurs, who quit Oasis in 1999 and was replaced by Gem.
Asked if they would record a track with him, Liam said: "Yeah man, why not? He's gotta bring his Freddie Starr wig along with him though. He's a geezer Bonehead, he's been to see some of the gigs."
Andy added to NME magazine: "Yeah, he's been to a lot of gigs. He's a lovely man. He's always welcome."
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The group are ready to start work on the follow-up to their debut album 'Different Gear, Still Speeding' and have promised their next record will be "life changing".
Liam said: "This one's gotta be like ... 11 f***ing classics on there. It's gotta be a life-changing record.
"I just think it's gonna be a bit more of a grand affair."
Andy added: "Looking back on the first one, we know how we can improve it. I still love it, I still think it's great, but we can better it."