  We construct a $d=11$ supergravity analogue of the open-closed string map in
the context of SL(5) Exceptional Field Theory (ExFT). The deformation parameter
tri-vector $\Omega$ generalizes the non-commutativity bi-vector parameter
$\Theta$ of the open string. When applied to solutions in $d=11$, this map
provides an economical way of performing TsT deformations, and may be used to
recover $d=10$ Yang-Baxter deformations after dimensional reduction. We present
a generalization of the Classical Yang-Baxter Equation (CYBE) for rank 3
objects, which emerges from $d=11$ supergravity and the SL(5) ExFT. This
equation is shown to reduce to the $d=10$ CYBE upon dimensional reduction.
