This paper introduces and investigates the concept of almost quasi $(\tau_1, \tau_2)$-continuous multifunctions in bitopological spaces. The authors define a multifunction $F: (X, \tau_1, \tau_2) \to (Y, \sigma_1, \sigma_2)$ as almost quasi $(\tau_1, \tau_2)$-continuous if, for every $\sigma_1 \sigma_2$-open sets $V_1, V_2$ of $Y$ such that $F(x) \in V_1^+ \cap V_2^+$, there exists a $(\tau_1, \tau_2)$-s-open set $U$ of $X$ containing $x$ such that $F(U) \subseteq (\sigma_1, \sigma_2)$-sCl$(V_1)$ and $(\sigma_1, \sigma_2)$-sCl$(V_2) \cap F(z) \neq \emptyset$ for every $z \in U$. The paper also provides several characterizations of this property, including equivalent conditions involving $(\tau_1, \tau_2)$-s-open sets, $(\tau_1, \tau_2)$-r-open sets, and $(\tau_1, \tau_2)$-β-open sets. The results are derived using properties of bitopological spaces and multifunctions, and the proofs are detailed in theorems and lemmas. The research is financially supported by Mahasarakham University, and the authors declare no conflicts of interest.This paper introduces and investigates the concept of almost quasi $(\tau_1, \tau_2)$-continuous multifunctions in bitopological spaces. The authors define a multifunction $F: (X, \tau_1, \tau_2) \to (Y, \sigma_1, \sigma_2)$ as almost quasi $(\tau_1, \tau_2)$-continuous if, for every $\sigma_1 \sigma_2$-open sets $V_1, V_2$ of $Y$ such that $F(x) \in V_1^+ \cap V_2^+$, there exists a $(\tau_1, \tau_2)$-s-open set $U$ of $X$ containing $x$ such that $F(U) \subseteq (\sigma_1, \sigma_2)$-sCl$(V_1)$ and $(\sigma_1, \sigma_2)$-sCl$(V_2) \cap F(z) \neq \emptyset$ for every $z \in U$. The paper also provides several characterizations of this property, including equivalent conditions involving $(\tau_1, \tau_2)$-s-open sets, $(\tau_1, \tau_2)$-r-open sets, and $(\tau_1, \tau_2)$-β-open sets. The results are derived using properties of bitopological spaces and multifunctions, and the proofs are detailed in theorems and lemmas. The research is financially supported by Mahasarakham University, and the authors declare no conflicts of interest.