Consider following setup: A number of observations from a data source shall be compressed jointly prior to a forward transmission via several rate-limited links to a central processing unit. To design the respective quantizers, here, Mutual Information is chosen as the fidelity criterion and the broad-ranging structure of Multivariate Information Bottleneck is then aptly tailored to that purpose. This, indeed, not only yields a novel design approach for the considered distributed scenario but also paves the way towards perceiving the chance of leveraging this flexible conceptual frame in a vast variety of applications regarding digital data transmission. Explicitly, it immediately enables addressing various extensions of the presumed arrangement, incorporating the parallel construction of intertwined compression systems for several correlated sources.