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
Alexander Street Literature is a comprehensive, cross-searchable package of collections covering literatures of place, race, and gender. It includes poetry, short fiction, and novels, along with full-text plays and film scripts.
As a digital repository for the nation's great research libraries, HathiTrust brings together the immense collections of partner institutions. It provides long-term preservation and access services for public domain and in copyright content from a variety of sources, including Google, the Internet Archive, Microsoft, and in-house partner institution initiatives.