Associate Chief Justice John Rooke will rule on a joint request from the Crown and defence that Travis Baumgartner, 22, be sentenced to life in prison with no chance of parole for 40 years.
If the sentence is approved, it would set a precedent under legislation passed in 2011 that allows judges to hand out consecutive sentences to multiple murderers.
The sentence would be the harshest handed down in Canada since Arthur Lucas was executed in 1962 for the murder of a police informant.
Judges can refuse joint requests, but it rarely happens.
If Rooke agrees, Baumgartner would not face a parole board until 2052.
Baumgartner pleaded guilty Monday to one count of first-degree murder, two counts of second-degree murder and one count of attempted murder in the June 2012 robbery and shooting deaths of Michelle Shegelski, 26, Eddie Rejano, 39, and Brian Ilesic, 35, at HUB Mall, a student residence and indoor food court.
A fourth guard, Matthew Schuman, was critically injured in the shooting.
Baumgartner was arrested days later at a U.S. border crossing in British Columbia.