CLIO is the online catalog to Columbia University Libraries (including Barnard), but excluding Teacher's College and the Law Library who maintain their own catalogs. CLIO contains over 7 million records for books, online resources, journals & newspapers, conference proceedings, sound recordings & scores, videos, archival collections & oral history transcripts, online databases, maps & images, and more!
Some of these databases have lists of plays with where they're published, but many include the full text of plays.
To find plays as ebooks in CLIO, try a search for online books. You can always limit by language, publication date, and put in a search term (e.g., "monologues") to help narrow your search