The theory is given and a numerical analysis is presented of propagation of piezoelectric interfacial waves along a perfectly conducting plane that separates two piezoelectric half-spaces of different crystallographic orientations or two half-spaces of different piezoelectrics. In the case of slightly different orientations (half a degree in each Euler angle), it is found that the coupling coefficient is in general less than in the case of two half-spaces of the same orientation, but still large. For example, it is 3.40% for lithium niobate (instead of 3.50%), 0.85% for dilithium tetraborate (instead of 0.90%), 0.15% for langasite (instead of 0.20%). In the case of two half-spaces of arbitrary different crystallographic orientations (lithium niobate and lithium niobate), and two half-spaces of different piezoelectrics (dilithium tetraborate and lithium niobate), it is found that the coupling coefficient may be quite large for some crystal cuts (correspondingly 2.25% and 1.45%), although for the majority of crystal cuts the waves do not exist.