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Among non-Psittacopasserans (Psittacopasseraeans?) heterospecific vocal mimicry doesn't seem to be as versatile. As far as I'm aware (again, feel free to correct me), recorded instances tend to only mimic one model, and do not appear to be learned (e.g. burrowing owl chicks imitating rattlesnakes as defense), having more in common with more "traditional" forms of mimicry than what, say, a lyrebird does. Something like this might be more plausible for a non-neornithean dinosaur.
(Cuckoo chicks are a bit of an outlier here, as they can mimic two other species (i.e. potential hosts) and adjust their begging calls for maximum response in the host. The mimicking per se doesn't appear to be learned, though, and nest parasitism seems to drive this)
Araya-Salas, M., Wright, T. 2013. Open-ended song learning in a hummingbird. Biology Letters, 9(5).
Dalziell, A.H., Welbergen, J.A., Igib, B., Magrath, R.D. 2015. Avian vocal mimicry: a unified conceptual framework. Biol Rev Camb Philos Soc., 90(2):643-68.