Let M be a model category that is a Grothendieck topos. Let $T$ be a multisorted finitary algebraic theory. Does there exist the right transferred model structure on the category of $T$-algebras in $M$? (in the sense adjunction with $M^S$, where $S$ is the set of sorts of $T$).

Intuitively, I tend to answer "no" and would like to know an example of a topos and a model structure on it, for which the mentioned transfer does not exist.

Related question:https://mathoverflow.net/questions/440278/what-should-be-required-from-a-model-category-that-the-category-of-algebraic-obj