Higher education in Taiwan has expanded dramatically in the previous three decades. The number of students enrolled in higher education institutions has nearly quadrupled from 348,290 (1984) to 1,345,000 (2013). In 2012, the gross entrance rate of higher education reached 84.43%, which is higher than most higher education systems in Asia. Higher education that transforms from a mass system to a universal system raises public concern regarding its quality. This study explored situations arising from a change to right-based higher education, particularly in pursuing a balance between quality and quantity in the process of establishing research universities. We selected two top public universities to illustrate how institutional arrangements play crucial roles in balancing quality and quantity. The findings reveal strong pressure for a world-class university within both universities, whereas student opinions reflect a neglect of instruction. In this case, faculty focused less attention on teaching compared to their research. These two universities should focus more efforts on teaching to balance quality and quantity toward a world-class research university.