Let's consider a very simple table:
\begin{tabular}{c || c | c}
& x & y \\ \hline \hline
a & 1 & 2 \\ \hline
b & 3 & 4
\end{tabular}
This produces the following table:
Notice that at the intersection of the double lines (top left), the vertical lines break and the horizontal lines don't. Is there a way to flip this behavior, i.e. make the horizontal lines break while the vertical lines go through?