This ensemble is named after 20th-century composer Arnold Schoenberg’s seminal work Pierrot lunaire, which includes the quintet of instruments above with a narrator (usually performed by a soprano).
More frequent are works that introduce additional instruments, typically more strings, and especially percussion which obtains a small, and inexpensive, chamber ensemble with three families of instruments represented.
Doublings are a standard compositional device used to extend an ensemble instrumental color.
Other common doublings might include E♭ clarinet (as in Carter's Triple Duo), alto flute.
Christopher Dromey, The Pierrot Ensembles: Chronicle and Catalogue, 1912-2012 (London: Plumbago, 2013).