  In this study, we present several improvements of the non-relativistic
Friedrichs-Lee model with multiple discrete and continuous states and still
retain its solvability. Our findings establish a solid theoretical basis for
the exploration of resonance phenomena in scenarios involving the presence of
multiple interfering states across various channels. The scattering amplitudes
associated with the continuous states naturally adhere to coupled-channel
unitarity, rendering this framework particularly valuable for investigating
hadronic resonant states appearing in multiple coupled channels. Moreover, this
generalized framework exhibits a wide-range applicability, enabling
investigations into resonance phenomena across diverse physical domains,
including hadron physics, nuclear physics, optics, and cold atom physics, among
others.
