On the positve definiteness of a particular matrix and inverse

Question

I have the following question. Let $M=BAC=M^T$ where $B\in\mathbb{R}^{m\times n}$, $C\in\mathbb{R}^{n\times m}$ and $A\in\mathbb{R}^{n\times n}$ invertible. Suppose $M$ is positive definite, $B$ is full row rank, $C$ is full column rank and $B\neq C^T$.

Question: Is there any possible scenario (potential additional conditions for $A$, $B$ or $C$) where I can conclude that the matrix $W=BA^{-1}C$ is also positive definite as a consequence of the positive definiteness of $M$?

Thanks in advance!

Best,

N.