  Bi-incomplete Tambara functors over a group $G$ can be understood in terms of
compatible pairs of $G$-transfer systems. In the case of $G = C_{p^n}$ , Hill,
Meng and Li gave a necessary and sufficient condition for compatibility and
computed the exact number of compatible pairs. In this article, we study
compatible pairs of $G$-transfer systems for the case $G = C_{p^rq^s}$ and
identify conditions when such transfer systems are uniquely compatible in the
sense that they only form trivially compatible pairs. This gives us new insight
into collections of norm maps that are relevant in equivariant homotopy theory.
