Alberta's opposition parties say the University of Calgary should provide an explanation about arrangements with a private clinic located on university property.
The Helios Wellness Centre was the focus of some accusations about queue-jumping at an inquiry last week.
It is located near the Foothills hospital in a teaching building that belongs to the university.
Two Calgary doctors testified last week they heard the clinic was opened to provide a reward for major donors to the university.
In previous testimony at Alberta's health care queue-jumping inquiry, a clerk at the Forzani and MacPhail Colon Cancer Screening Centre testified patients from the clinic were given preference over other people waiting for screening.
Wildrose MLA Kerry Towle says Albertans deserve answers from the University of Calgary.
"I think until they do that, there's going be a cloud above them and I don't think they want that."
NDP leader Brian Mason is calling for a wider look at the administration.
"We need to find broadly based review of the University of Calgary and its administration."
The University of Calgary has issued two written statements, saying it will not make full comments until the inquiry is over.
On Monday night, Alberta Health Services issued a written statement about what it calls "troubling evidence" being given at the public inquiry.
Officials say senior AHS staff are working with the Forzani and MacPhail Colon Cancer Screening Centre to ensure the necessary processes are in place to provide appropriate access to services.
"Albertans can be assured that we understand the urgency and importance of the issues raised," said Dr. Chris Eagle, the president and CEO of Alberta Health Services.
The inquiry will resume in February.