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Austin Ainge says Celtics ‘like a lot of guys in this draft’

Syracuse’s Oshae Brissett (right) was one of six players who worked out for the Celtics Monday.file/rick bowmer/AP/Associated Press

The Celtics have the 14th, 20th, 22nd, and 51st overall selections in this month’s NBA Draft. It is quite unlikely that they will add four rookies to next season’s roster, but anything is possible.

“We’ve been down this road in the past few years where we’ve had lots of picks,” director of player personnel Austin Ainge said Monday. “It’s something you have to consider.

“Just so many other things will dictate whether that’s feasible or not, but we do like a lot of guys in this draft and there are scenarios when we would have three [first-round] guys and keep them all.

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“It’s certainly manageable on a 15- or 17-man roster now with two-way [contracts] to have some rookies.”

Having so many picks has made the predraft process slightly easier for the Celtics because agents are more willing to send their clients to Boston for workouts given the wide range that the team has covered.

Ainge said the Celtics have had 70 prospects come to their training facility so far, with plenty more scheduled.

“We try to get in guys of all different draft ranges and guys to evaluate for the future,” Ainge said. “You can only draft a few every year, but if you have them in, you get to know them, get to meet them.

“Then, if in three years from now, they play well in the G-League or Turkey, at least you’ve got to know them a little bit. We’re evaluating for many years in the future, as well as now.”

On Monday, the Celtics hosted a six-player workout with Virginia’s Ty Jerome, Tennessee’s Admiral Schofield and Jordan Bone, Syracuse’s Oshae Brissett, Illinois State’s Milik Yarbrough, and Jacksonville State’s Jason Burnell.

Jerome, one of the stars of the Cavaliers’ national title run, and Schofield are viewed as a potential late first-round picks.

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This is expected to be another wild summer for the Celtics’ front office. Kyrie Irving and Marcus Morris will be unrestricted free agents, Terry Rozier will be a restricted free agent, and Al Horford and Aron Baynes will have the ability to opt out of the final year of their deals.

With so many moving parts, as well as the chance to sign free agents from other teams, it makes the draft somewhat complicated because the Celtics will not know all the gaps they need to fill.

“I have been a big proponent of switching the [date of the] draft and free agency,” Ainge said. “I think that most teams build from veteran players first. If you have a top-five pick, you’re most likely a rebuilding team, so free agency isn’t affecting that.

“And then all of the other teams, you more likely are fitting in draft picks in and around a veteran core group. So I think the calendar should follow our decision-making tree. So I think it should be switched.”

Adam Himmelsbach can be reached at adam. himmelsbach@globe.com.