Our extant texts never give a fully comprehensive or representative impression of classical literature. Fragments are valuable because they tell—or hint at—a different story. They represent vestigial traces of a counterfactual alternative version of literary history, and they offer tantalizing glimpses of voices or varieties of human experience that were (accidentally or deliberately) excluded from the classical canon. To ‘think fragmentarily’ is to think beyond the canon and to question traditionally dominant modes of thought. This article uses a neglected fragment of Damoxenus (fr. 3 PCG) as a case study for ‘fragmentary thinking’. This extraordinary fragment reveals that Damoxenus’ comedy dramatized a homosexual love story, in sharp contrast to the familiar heteronormative marriage plots of Menander and other Greek and Roman comic playwrights. Careful examination of a single fragment can prompt us to re-examine conventional scholarly narratives of sexuality in New Comedy.