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 \( \mathfrak{g} \) . In the YB case, our construction produces one integrable deformation for each pair ( \( \mathcal{R} \) , E), where \( \mathcal{R} \) is an antisymmetric bilinear operator on \( \mathfrak{g} \) 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 ( \( \mathcal{R} \) , \( \overset{\sim }{\mathcal{R}} \) , E), where \( \overset{\sim }{\mathcal{R}} \) is another antisymmetric bilinear operator on \( \mathfrak{g} \) obeying the 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.
