  It has recently been demonstrated that the Classical Yang-Baxter Equation
(CYBE) emerges from supergravity via the open-closed string map. Thus, given
any solution with an isometry group, there exists a deformed solution based on
an $r$-matrix solution to the homogeneous CYBE. In this work, we argue that the
CYBE emerges exclusively from the NS sector, while the RR sector acts largely
as a spectator that supports the spacetimes. Moreover, shifting the dilaton by
a constant, one can incorporate $r$-matrix solutions to the modified CYBE, but
only for original geometries that are a direct-product of coset spaces. We
illustrate our solution generating technique with deformations of $AdS_3 \times
S^3 \times M_4$, where $M_4 = T^4$ (K3) and $S^3 \times S^1$, and explicitly
construct one and two-parameter (integrable) q-deformations that are solutions
to generalised supergravity.
