In theatre, we often use the term "multicultural" to describe authors who are non-white or who have non-European heritage.
But "Multicultural Theatre" includes playwrights writing from many different traditions and cultures!
In the library catalog, one way to find plays by multicultural playwrights is to do a subject search that combines the ethnic group you're interested in with the word, "Drama."
For example, to find plays by Asian American playwrights, search for:
For plays by Hispanic playwrights, search for:
To find plays by African Americans:
Can't find what you're looking for? There are lots of other ways to search for plays~
Black Theater: A 20th Century Collection of the Work of Its Best Playwrights by 
Contemporary Plays by Women of Color: An Anthology by 
Who's Who in Contemporary World Theatre by