I don't think the problem is with multiculturalism as such, Kachah is right, this is a euphemism. Australia officially adopts multiculturalism as a national ideology,.
and there are minimal problems here in terms of culture clashes (though obviously there's some, it generally doesn't disrupt ordinary life except in very unusual cases like the Cronulla riots). Most people find a balance between their heritage and integration into Australia. .
Europe's problem is not many cultures -- it is certain cultures which are in some ways incompatible with their own and cannot be easily reconciled.