Which types of knowledge-intensive business services firms collaborate with universities for innovation?

•Data from an original survey to investigate which types of KIBS firms collaborate with universities.•Science-based KIBS firms (KIBS firms engaged in a science, technology, innovation [STI] organizational mode of leaning) are active collaborators of universities for innovation.•KIBS firms engaged in a doing, using and interacting (DUI) mode of organizational learning and providing highly customized services also actively collaborate with universities for innovation.•KIBS firms co-create knowledge with universities differently than manufacturing firms.•Findings highlight the variety of roles that KIBS firms play in innovation networks with universities.