Baseline models have been used in the analysis of social networks as a way to understand how empirical networks differ from “random” ones. For the purposes of social network analysis, a “random” network is one chosen—at random—from a population of possible graphs derived from a given generating function. Although these principled hypothesis tests have a long history, many of their properties and extensions to multiple data structures—here, specifically two-mode data—have been overlooked. This article focused on applications of different baseline models to two data sets: donations and voting of the 111th U.S. Congress, and organizations involved in forums on watershed policy in San Francisco, USA. Tests using each data set, but with different baseline reference distributions, will illustrate the range of possible questions baseline models can address and the differences between them. The ability to apply different models and generate a constellation of results provides a deeper understanding of the structure of the system.