  Cavity-magnon polaritons (CMPs) are the associated quasiparticles of the
hybridization between cavity photons and magnons in a magnetic sample placed in
a microwave resonator. In the strong coupling regime, where the macroscopic
coupling strength exceeds the individual dissipation, there is a coherent
exchange of information. This renders CMPs as promising candidates for future
applications such as in information processing. Recent advances on the study of
the CMP now allow not only for creation of CMPs on demand, but also for tuning
of the coupling strength - this can be thought of as enhancing or suppressing
of information exchange. Here, we go beyond standard single-port driven CMPs
and employ a two-port driven CMP. We control the coupling strength by the
relative phase $\phi$ and amplitude field ratio $\delta_0$ between both ports.
Specifically, we derive a new expression from Input-Output theory for the study
of the two-port driven CMP and discuss the implications on the coupling
strength. Furthermore, we examine intermediate cases where the relative phase
is tuned between its maximal and minimal value and, in particular, the high
$\delta_0$ regime, which has not been yet explored.
