A simple approach is to first carry out a ($x$-dependent) unitary transformation of $A(x)$, such that all diagonal elements are zero. (This is always possible, see for example https://math.stackexchange.com/q/267192/87355 ) Then, you take
$$B=\begin{pmatrix}
1&0&0\\
0&2&0\\
0&0&3
\end{pmatrix},\;\;
C_{ij}(x)=\begin{cases}
0&\text{if}\;i=j\\
\frac{A_{ij}(x)}{B_{ii}-B_{jj}}&\text{if}\;\;i\neq j.
\end{cases}
$$