Let $G$ be a connected, simply connected simple complex algebraic group and let $\epsilon$ be a primitive $\ell$th root of unity with $\ell$ odd and coprime with $3$ if $G$ is of type $G_{2}$. We determine all Hopf algebra quotients of the twisted multiparameter quantum function algebra $\mathcal{O}_{\epsilon}^{\varphi}(G)$ introduced by Costantini and Varagnolo. This extends the results of Andruskiewitsch and the first author, where the untwisted case is treated.