A mid-major powerhouse. The defending national champions — potentially. Three other quality high-major programs.

St. John’s made significant upgrades to its non-conference schedule after so many complaints about last year’s slate. Released on Tuesday, it includes games for new coach Mike Anderson’s team against Arizona, Arizona State, West Virginia, Vermont, and possibly Virginia in the Hall of Fame Tip-Off tournament at Mohegan Sun. It also features games against locals Columbia, Wagner and St. Peter’s.

It’s quite a contrast to the run of cupcakes St. John’s faced a year ago, when the Red Storm’s only high-major opponent was Duke. This time the Johnnies will be tested by the time Big East play rolls around.

The Red Storm will play an exhibition game against Queens College on Oct. 30 and open the Anderson era against Mercer of the Southern Conference on Nov. 6 at Carnesecca Arena. Vermont, the defending America East champion, comes to Queens on Nov. 16.

For the third straight year, St. John’s will face Arizona State, this time in the Hall of Fame Tip-Off on Nov. 23. Sun Devils coach Bobby Hurley was the top target for St. John’s after Chris Mullin stepped down as head coach, but he opted to stay out west. The Johnnies will face either Virginia or Massachusetts the next day and will meet West Virginia in their first game at the Garden on either Dec. 7 or 8 in the inaugural Big East-Big 12 Challenge.

The non-conference schedule wraps up Dec. 21 with a trip to the Bay Area to face Arizona in the Hall of Fame Al Attles Classic at the Warriors’ new arena, the Chase Center.

St. John’s will host Cleveland State ttransfer Rasheem Dunn for an official visit starting Thursday. The 6-foot-2 guard from Brooklyn went to high school with former Johnnies star Shamorie Ponds. He has visited Siena and Arkansas, among others. St. John’s has one open scholarship remaining for the coming season.