We combine the Yang-Baxter (YB) and bi-Yang-Baxter (bi-YB) deformations with higher-spin auxiliary field deformations to construct multi-parameter families of integrable deformations of the principal chiral model on a Lie group G with semi-simple Lie algebra g. In the YB case, our construction produces one integrable deformation for each pair (R,E), where R is an antisymmetric bilinear operator on g
Nearby in the stack
obeying the modified classical Yang-Baxter equation and
E
is a function of several variables. In the bi-YB case, the pair becomes a triplet
(R,R~,E)
, where
R~
is another antisymmetric bilinear operator on
g
and obeys the non-split inhomogeneous modified classical Yang-Baxter equation. We show that every model in these families is (weakly) classically integrable by exhibiting a Lax representation for their equations of motion.