There's no definitive, readily available number for how many colleges opened in the United States between 1880 and 1900. The data collection methods and definitions of "college" varied across that period. Furthermore, a comprehensive, centralized database tracking all college openings during that time doesn't exist.
To find even an approximation would require extensive research across individual state archives, historical society records, and potentially old college yearbooks and newspapers. Such a project would be quite substantial.