Athletic director Kevin White thinks the Blue Devils can do it.
The football team reached the Atlantic Coast Conference championship game, as did the historically strong men's and women's basketball teams.
The men's lacrosse team and women's golf team claimed national titles and the field hockey team reached the NCAA championship game.
In an interview with The Associated Press, White called it a "really good year" but added that "we were really close to having one of those really great years."
To White, that involves reaching the top five in the Directors' Cup — presented annually to the top overall college athletic program.
In the latest rankings, Duke was No. 7.
That's Duke's highest ranking since it was fifth in 2011, and among ACC schools, only No. 2 Notre Dame ranked higher.
"That's a benchmark that we're shooting for," White said. "We think we belong in that neighborhood."
Plenty of things came together for the Blue Devils in a wide variety of sports.
"There's a lot of indicators to suggest that it wasn't a fantastic year, but a really good year," White said. "And it had a chance to be one of the really historic special years. And I'm hoping that (2014-15) can be all of that and then some."
Nine of its teams were ranked in the top 10 at some point during the year, including the perennially powerful men's and women's basketball teams.
Duke became the first school to have its football and both basketball teams reach ACC championship games — though the Blue Devils also lost all three. The baseball team would have reached one, too, if not for an extra-inning loss in round-robin pool play.
The men's lacrosse team claimed its second consecutive national title and third in five years. The women's golf team won its sixth NCAA title and its first since going back-to-back in 2006 and '07.
But the biggest breakthrough came in football — where coach David Cutcliffe's team continued its transformation from perhaps the worst power-conference program to Coastal Division champion.
Duke set a program record with 10 wins before losing to eventual national champion Florida State in the ACC title game and reaching its second consecutive bowl game — the first time the Blue Devils have done that.
"It's no surprise to me that season  was better than season '12 and I think the '14 team has a chance to be more talented than the '13 team, and I suspect the '15 team has a pretty good chance to be even more talented than the '14 team," White said. "The trajectory is really good."
And now it won't be too long until the rebuilt program has some rebuilt facilities.
After the football season, work will begin on giving 85-year-old Wallace Wade Stadium a face-lift for the 2015 season. The track will be removed, the playing field lowered and the stands will be extended closer to the field.
The press box — which doubles as the school's sports medicine offices — will be demolished and rebuilt over a roughly 18-month period to include luxury suites and club seating, and the open end of the stadium's horseshoe will be bowled in to bring capacity to just under 44,000.
The Wallade Wade Stadium project was supposed to have begun after last season, but routine construction delays forced a delay, White said. The school already moved some practice fields to allow for the construction of a new track and field stadium.
Planned improvements at Cameron Indoor Stadium during the next couple of years include a new lobby, renovated locker rooms and facilities for players and coaches, plus a plaza to connect it with the football stadium and the Yoh Center, which houses the football offices.
"We've kind of got the sweats off and we're really starting to perspire as we think about Cameron and Wallace Wade," White said. "But we needed to do a lot of projects to kind of put us in a position to move forward. ... They allow us to go into the stadium and do those other things."