Let's assume the minimum necessary conditions for the following expression to be well-defined: $$-\frac{1}{2} \mbox{Tr} \left(\Sigma^{-1}\left(\Lambda+\Phi -\Psi W- W\Psi^\intercal+W(\Xi+V^{-1})W^\intercal \right)\right)$$
where $\mbox{Tr} (\cdot)$ is the trace of a matrix.
Is there any way to rewrite the above expression as
$$-\frac{1}{2}Tr\left(g(\Sigma^{-1})+f(\Sigma^{-1},W)\right)$$
where $$f(\Sigma^{-1},W)= B_{W\Sigma} A_{\Sigma}^{-1}B_{W\Sigma}^\intercal C_{\Sigma}^{-1}$$
meaning, $B$ is a matrix expression depending on $W$ and $\Sigma$, and $A$ and $C$ cannot depend on $W$.