  Nonlinear response signatures are increasingly recognized as useful probes of
condensed matter systems, in particular for characterisation of topologically
non-trivial states. The circular photogalvanic effect (CPGE) is particularly
useful in study of topological semimetals, as the CPGE tensor quantises for
well-isolated topological degeneracies in strictly linearly-dispersing band
structures. Here, we study multiplicative Weyl semimetal band-structures, and
find that the multiplicative structure robustly protects the quantization of
the CPGE even in the case of non-linear dispersion. Computing phase diagrams as
a function of Weyl node tilting, we find a variety of quantised values for the
CPGE tensor, revealing that the CPGE is also a useful tool in detecting and
characterising parent topology of multiplicative topological states.
