IPA: /ˌɪntəˈkɒlɪdʒiˌeɪt/
KK: /ˌɪntərkəˈlɪdʒiˌeɪt/
Relating to activities or competitions that involve two or more colleges.
The intercollegiate debate competition attracted participants from several universities.
Intercollegiate → It is formed from "inter-" (meaning between) and "collegium" (from Latin, meaning a group of colleagues or associates). The word describes activities or competitions that occur between different colleges or institutions.
Think of activities that happen 'between' ('inter-') different 'colleges' ('collegium') — that's what intercollegiate means.