interuniversity
adjective
in·ter·uni·ver·si·ty ˌin-tər-ˌyü-nə-ˈvər-sə-tē 
-ˈvər-stē
variants or inter-university
: existing, occurring, or shared between two or more universities
interuniversity collaboration
interuniversity competitions
an interuniversity program
Word History
First Known Use
1860, in the meaning defined above