Schoenberg correspondence for multifaced independence

We extend the Schoenberg correspondence for universal independences by Schürmann & Voß to the multivariate setting of Manzel & Schürmann, covering, e.g., Voiculescu's bifreeness as well as Bożejko & Speicher's c-free independence. At the same time, we free the proof in the univariate situation from its dependence on Muraki's “5 Independences Theorem”.