The conjecture on extensions of ${\sf S}^1_2$ mutually interpretable with Tarski extensions

Let $A$ be finitely axiomatized, consistent, and sequential, and let $N:{\sf S}^1_2\lhd A$. Write $A+{\sf TB}^{-}_N$ for the corresponding Tarski-biconditional extension. Mutual-interpretability conjecture. There is no extension of ${\sf S}^1_2$ that is mutually interpretable with $A+{\sf TB}^{-}_N$. The statement is proposed as a possible negative instance of the open question whether every sequential theory is mutually interpretable with an extension, in the same language, of ${\sf S}^1_2$.