As the US and the rest of the world face a growing need for affordable and accessible higher education, we must more deeply examine the scalability of our universities: how do they change with size? How do different institutional types vary? What makes ASU number one in innovation? At least two of these questions have immediate relevance to not only higher education, but political economy and sustainability as well. We apply to institutions the exciting complex systems framework of scaling, which has led to deep theoretical insight into the structure of biological systems and cities (West, Brown and Enquist 1997, Bettencourt 2013). First we group universities into seven distinct sectors, from public research universities to professional schools. Then we examine the returns to scale of university revenues, expenditures, and graduation rates, by correlating these key variables versus total enrollment. We discover that the sectors exhibit some important similarities, but overall leverage different economies of scale to serve their own priorities. These results imply shared mechanisms and constraints among the entire class of institutions. Furthermore, the uniqueness of each sector reveals their "speciation" into diverse institutional models, offering a fresh (though limited) first look at their scale-dependent complementary roles and competitive advantages. Accordingly, we outline what additional data and analyses might sufficiently strengthen these results to make recommendations, at levels ranging from student and family decisions to individual university strategies to sector-wide and system-wide policies. Promising future directions include longitudinal analysis of university growth patterns, detailed outlier analysis, and deeper theoretical investigation of mechanisms that drive the observed scaling.