  We provide a general treatment for the temporal coupled-mode theory with
arbitrary numbers of modes and ports, and derive tight bounds for the coupling
phases in addition to coupling strengths under time-reversal symmetry. We
report trade-offs between the cardinalities of the reciprocal regions of the
resonant coupling strengths versus phases. We discover that time-reversal
symmetry enforces projected generalized reflections in the background to cancel
out completely. In double-port systems, the reciprocal regions of the coupling
phases span a quarter of the nonreciprocal regions for any non-hidden mode.
