I’m looking for bands with more than 1 member from more than 1 country.
Most famous example is Fleetwood Mac - 2 Americans, 3 Brits. Must be more examples.
(There are lots of bands who have one guy/girl from a different country than the rest of the band, not looking for those. Pretenders is 1 example)
Santana. Carlos was Mexican, and percussionist Jose “Chepito” Areas was Nicaraguan. The others in the group were American.
Does it have to be two or more from each country, or does having three different countries represented by at least one member count?
2 or more from each country , that is what makes it pretty rare.
Dragonforce has had members from England, Scotland, South Africa, France, Hong Kong, New Zealand and Slovenia.
Foreigner’s line-up on their first two albums was three Americans (Lou Gramm, Al Greenwood, Ed Gagliardi) and three Britons (Mick Jones, Ian McDonald, Dennis Elliot). For their third album, bassist Gagliardi was replaced by Englishman Rick Wills.
The current version of King Crimson has four Brits (Robert Fripp, Mel Collins, Jakko Jakszyk, and Gavin Harrison) and three Americans (Tony Levin, Pat Mastelotto, Bill Rieflin).
Travelling Wilburys:
Lynne, Harrison - UK
Dylan, Orbison, Petty - USA
CSNY . . . US, UK, and Canada.
ETA: just re-read the OP and realized I missed the ‘at least two members each from at least two countries’ stipulation. I retract CSNY.
AC/DC has (or has had) members from the UK as well as from Australia, I think.
CSNY: two Americans, a Brit, and a Canadian.
Badfinger had two English and two Welsh members.
The Who in its latter-day incarnation counts for partial credit - four Englishmen (Roger Daltrey, Pete Townshend, Simon Townshend, and Zak Starkey), one Welsh-Italian (Pino Palladino), and one American (John ‘Rabbit’ Bundrick).
Dragonforce have already been mentioned - their current lineup consists of two Englishmen, a Hong Konger, an Italian, a Frenchman, and a Ukranian, and previous members have hailed from Scotland and South Africa.
U2 - two from Ireland (Bono, Mullen). two from England (Edge, Clayton)
The Pogues - Shane, Spider and Jem from England, Cait was born in Nigeria, Terry and Chevron Irish
Obviously in these examples, where people are from, and where they identify with, is a whole other question.
The Beatles with Billy Preston 
Van Halen - 2 Dutch and 2 Americans (in the original lineup at any rate)
Dethklok: three Americans, one Norwegian, one Swede.
The mid-1990s incarnation of Power Station had two Brits - Robert Palmer and Andy Taylor - and two Americans - Tony Thompson and Bernard Edwards - although Edwards died before he had a chance to tour with them. This lineup made one album though.
Black Sabbath in 1980-81 had Americans Ronnie James Dio and Vinny Appice with Brits Tony Iommi and Geezer Butler. This lineup returned in 1990-92.
Jimi Hendrix Experience - Jimi was American, Noel and Mitch British.
