Fundamental issues about the coupling of twin supersonic jets of complex geometry are examined. It is shown that screech tones from twin rectangular nozzles with double-beveled exit geometries can couple. Unlike coupling of twin rectangular jets of uniform geometry, the coupling here is more intricate because simultaneous multiple frequencies with a different spanwise modal structure are present. The coupling produces two frequencies, one of which is lower than the screech frequency of either jet. Although many coupling modes are kinematically permissible, the twin jets prefer two specific modes, and in some cases these two coupling modes coexist at different frequencies. Despite the geometric complexity we can effectively predict frequencies of tones from both single and twin coupled jets using the waveguide approach. It is hoped that these results and insights will assist those simulating screech for the purpose of tailoring shock-containing complex twin jets that minimize sonic fatigue failure of aircraft structures.