Matthew Reilly's Jack West Jr novels. Seven Ancient Wonders had the team comprised of commandos hailing from Australia, UAE, Spain, Jamaica, Israel, Ireland (2 of 'em) and New Zealand, with a Canadian professer and Egyptian girl.
Tom Clancy's novel Rainbow Six, which spawned a slew of video games, is centered around a NATO + Israel Multinational Team, based in England albeit led by Americans.
The Ender's Game novels, particularly the Shadow arc, features a raft of child warriors from around the globe (the Netherlands, Spain, Australia, England, China, India, etc.).
Ender is the son of a Pole and a Mormon, Bean is Greek/Ibo from the Netherlands, Alai is North African, Dink is Dutch, Carn is an Aussie, Crazy Tom is a Brit, Dumper is Quechua, Fly Molo is from the Philippines, Hot Soup is Chinese, Petra is Armenian, Shen is Japanese, Vlad is Belorussian, Bonzo is Spanish, Rose De Nose is Jewish, Suriyawong is Thai, Virlomi Indian. Most of them end of commanding Armies against each other and then exiled off Earth as the first governors of the colonies.
The prequel novels have the Mobile Operations Police, a force made up of the best of the best from top agencies and special forces branches in various countries. When Captain Wit O'Toole, the commander of the unit, first arrives to New Zealand to recruit a number of "Kiwi" soldiers as MOPs. When the commander of a NZSAS base doubts the need of his country to get involved with the MOPs, O'Toole plays the politician and explains that they go to places where politics prevents most developed nations from interfering. If at least one members of the unit is from New Zealand, then the country can get credit for helping out. It's implied that the MOPs help form the International Fleet after the First Invasion.
Phoenix Force is an internationally operating (but US Government-controlled) anti-terrorist team selected from the world's best soldiers and operatives. They include Israeli veteran Yakov Katzenelenbogen, Canadian demolitions expert and security engineer Gary Manning, Japanese martial arts and electronics expert Keio Ohara, ex-SAS soldier and pilot David McCarter, and Rafael Encizo, a Cuban survivor of the Bay of Pigs invasion. When Ohara was killed and Katzenelenbogen retired their numbers were made up with SWAT member Calvin James (Black American) and Somalia/Gulf War veteran T.J. Hawkins (a Southerner). The team has used the assistance of John Trent, a Japanese-American ninjitsu master; and German Karl Hahn, former GSG 9 operator turned BND agent.
Contact had the Five, representatives from Earth who were chosen specifically to talk to the aliens. There's someone from India, the United States, the Soviet Union, China, and someone from an African nation.
Andrew Vachss's Burke books have the white American Burke, Chinese Mama Wong, Mongolian Max the Silent, black The Prophet/Prof, Jamaican Clarence and then some.
The hero's party in the Belgariad includes one member of each non-evil ethnic group on the continent, even the ones thought to be extinct.
In the sequel, some of the western groups are dropped but they gain a Nyissan (Sadi) and an Angarak ('Zakath).
Notably, most of the members of the team are also exceptional representatives of their nation's hat, thus symbolising that culture as a whole: Mandorallen is the strongest knight, Silk the best spy, Sadi the best poisoiner, etc.
Eddings does the same thing in The Elenium, with a team consisting mainly of a member of each of the continent's four orders of church knights (one from each dominant country), plus two Styrics and a few accessories. Then the same thing happens again in The Tamuli.
Remote Man is about a group of five teenagers who band together to bring down a wildlife smuggling operation: Ned (Australian, but living in Massachusetts for most of the book), Kate (Australian), Rocky (American), Cleverton (Jamaican) and Yvette (French). Most of the communication between them is through e-mail and chatrooms.
A Sailor Of Austria is the story of an Austro-Hungarian U-boat in WWI, carrying a crew of eleven that speaks nine different languages.
In X-Wing: Rogue Squadron the eponymous fighter squadron is partly reconstituted as one of these for political reasons (i.e. to coax wavering planets to join the New Republic or appease grumpy politicians, they'd put a pilot from their planet in the Rogues). The team ends up with two Corellians, an Alderaanian, a Bothan, a Rodian, a Shistavanen, a gal from Kessel and another from Bespin, a Twi'lek, and a Tatooinian. The most blatantly political one is that they end up with two Thyferran pilots, one with family connections to each of the two major bacta cartels.
In The Amazing Adventures of Kavalier and Clay, the Escapist is a European-born American, aided by the Austrian Dr. Alois "Big Al" Berg, the Chinese Miss Plum Blossom, and Omar, who is from some fictional North African country but looks very much Indian.
The students in Idlewild are intentionally genetically and culturally varied as their designers wanted to incorporate as many possibilities for survival as possible.
In the Countdown series, M Day initially began as an all-American force, but then slowly picked up various nationalities; by the time of book two, they have American, British, Canadian, Chinese, Guyanan, Russian, Gurkha soldiers, and even some Cuban sailors who defected.
The collaborative Russian sci-fi novel The Road to Mars (written by 15 authors) involves a crew of six being sent on humanity's first manned mission to the red planet. The mission is a joint effort between NASA, ESA, and Roscosmos, with the crew made up of two Russians, two Americans (one of whom is black), a Frenchman, and an Italian. Notably, they are the second backup crew. The original crew was grounded after two of its members died in a plane crash, and the first backup crew was unable to achieve orbit, leaving the third crew the only ones who can get to the ship Ares in a reasonable timeframe. The multinational crew has to not only get to Mars but beat the Chinese Millennium Boat, which averts this trope by having only a crew of two, both being Chinese.