Barbour joins the group as USC searches for a new athletic director.
The club will grant members an open bar, private restrooms, Wi-Fi, and a unique view of the team taking the field at home games.
Williams will officially step into the role on June 12.
Adams spent seven seasons at Villanova before joining the Denver Broncos in 2022.
Michigan State confirmed the alteration after ESPN first reported the date change.
"We have many new players with a brand-new staff and the time together will hopefully create bonds and relationships that we will value very much."