Jeffrey Alexander argues that out-groups can get included in civil society in three ways: assimilation, hyphenation, and multiculturalism. These modes of incorporation form a spectrum. Every group experiences a bit of each - which predominates in each era and for a specific group is an empirical question. Alexander cites the case of Jews in America as a successful case of incorporation that moved from assimilation prior to the twentieth century, through hyphenation in the early part of the twentieth century, to a remarkable form of multicultural acceptance of difference since World War Two.
Alexander treats the middle term of this sequence as hyphenation, which he says is better known as the melting pot. Yet on the face of it, hyphenating a group's identity, or amalgamating it into the whole, are different processes. They may be opposites. Both ideas were, in fact, developed by Jewish Americans to understand and theorize Jewish-American experience.
In Israel Zangwill's popular play, "The Melting Pot," all the national identities that the peoples of America bring are melted together to form an amalgam, an alloy, that is different from any of the source identities. This is the critical difference between amalgamation and assimilation. Even when there is a clear difference between the host society and the newcomers being incorporated, it makes a big difference whether the outcome of incorporating the out group leaves the host society unchanged. The host society assimilates the out group by stripping off their cultural distinctives, leaving only their naked personhood to be remade in the host's image. The host society amalgamates the out group, by contrast, by melting both together to produce something new, including a new culture for the host society.
"Pluralism" as a social theory was primarily developed by Horace Kallen. He argued for hyphenated identities -- a group could be both loyally American and still distinctively itself. The two identities, though, are clearly in a hierarchy: American is the overarching identity, modified by the hyphenated variant. In becoming Newcomer-Americans, the newcomers have clearly given up some elements from the old country. They have gained a new way of being Newcomers (whatever that means in a cultural sense).
Alexander argues, and I agree, that the civil sphere of the United States is actually pretty healthy. We are good at incorporating newcomers. We are getting better at incorporating them (us) in a way that makes them real Americans, but with the distinctive flavor of their group culture. The outsider is converted from “a strange intruder to a familiar friend.”
Alexander rejects the extreme kind of multiculturalism that sees each group remaining separate. He does not denigrate America society as inherently oppressive, to be resisted in the name of identity politics.
As I look at it, Alexander's multiculturalism (the good kind) is the same as what he describes as hyphenated incorporation. Hyphenation is not the same as the melting pot. Hyphenation is the same as multiculturalism.