Hofstra and Stony Brook, who will play each other in their annual Long Island rivalry game Tuesday night, both will regularly face national-caliber teams as part of an ambitious plan for college basketball at the new Nassau Coliseum.

The plan also includes a recently filed application to host the opening rounds of the 2019 NCAA Tournament and an effort to attract major conference tournaments, according to Brett Yormark.

Any conference is on the table, said Yormark, CEO of Brooklyn Sports & Entertainment, which operates the Barclays Center and controls and manages the Coliseum.

“Our goal is to dream big,” Yormark said Sunday as Hofstra played Kentucky before a lively crowd of 7,514 in Brooklyn. Pointing out that Barclays Center will host the ACC championship tournament this March, he added, “We dream big and try to deliver. So far in Brooklyn we have, and my expectation is we’ll do the same out there.”

His group announced last month that Stony Brook will play Maryland, and Hofstra will meet 2016 NCAA champion Villanova (with former Hofstra coach Jay Wright) in 2017, the debut year of the refurbished Coliseum. Yormark emphasized on Sunday that those games will be only the start of a push to have the local teams play big-name opponents, as well as scheduling neutral-site games between major colleges.

“We don’t randomly select teams. We want the best teams but we also want them to have some connection to the marketplace, whether it’s recruits on the team or alumni or otherwise,” Yormark said. “The whole goal when we open the Coliseum is to glamorize local schools and to bring attention to the marketplace. The games will be nationally distributed. By more people watching nationally — not just fans, but coaches and athletic directors — they will recognize the Coliseum as a go-to place for college basketball.”

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With the Coliseum still under construction, Hofstra’s arena will be the go-to place Tuesday night when the two Long Island teams meet for a third consecutive season in their revived series. Each side has won one, and both games have been close.

“It’s a great rivalry game, we can’t wait to play again,” Hofstra coach Joe Mihalich said at Barclays Center after the 96-73 loss to No. 6 Kentucky. “We want to get this taste out of our mouth. We want to build on what happened today. Hopefully some of our Hofstra people will come out to the game because it has the makings of a good college basketball night.”

Stony Brook also is coming off an emotion-packed game, a 71-66 loss at home to Rutgers and former Stony Brook coach Steve Pikiell at home on Saturday. Roland Nyama, who has been with the Seawolves for the rivalry the past two years, said, “We don’t want to lose against Hofstra.”