Given a countable group G, we say that a metrizable flow Y is model-universal if by considering the various invariant measures on Y, we can recover every free measure-preserving G-system up to isomorphism. This notion was introduced by Weiss, who showed that a minimal model-universal flow exists for every countable group G. In this note, we provide a new, streamlined construction, allowing us to show that a minimal model-universal flow is far from unique.