Reading Measure for Measure through the logic of substitution has been a long-standing critical tradition; the play seems to invite topical, political, and religious parallels at every turn. What if the logic of substitution in the play goes beyond exchange and seeks out a triadic logic instead? This insistent searching for the triad appears most notably in the performance of Measure for Measure by Cheek by Jowl (2013–2019). Cheek By Jowl’s strategies of touring, simplicity, movement, and liberation create a dynamic and ever-evolving performance. This article puts Cheek by Jowl’s performance of Measure for Measure in conversation with C.S. Peirce’s (and subsequent theorists) explorations of triadic logic with Puttenham’s rhetoric of traductio (repetition with variation, and "tranlacing"), in addition to critical work on substitutions in the play. Tracing the superfluity of substitutions in rhetoric and performance of the play allows us to see how the play refuses binaries, and energizes triadic logic as a means to liveness in performance. Both Shakespeare’s play and the Cheek By Jowl production use a triadic structure which suggests the Trinity, foregrounding the body as a site of mediation and liveness.