The best way to make this argument is to say that multiculturalism will allow more people to feel that they are a part of the society and that they are valued and accepted.
If we do not allow multiculturalism, we are telling all people outside the mainstream that their ways are not acceptable and that they must change in order to be good members of our society. This (you can argue) makes them feel that they are not good enough; that we do not approve of them or value them. In such circumstances, they will never feel that they are part of our society and cohesion will be lacking.
If, by contrast, we embrace multiculturalism (the argument goes), we make newcomers feel welcome. They come to feel like they really belong in our country and are a part of our society. This leads to greater social cohesion.
One might use the argument in Federalist 10. Many factions tend to separation of power.