"Everything is still on the table," Kupchak said Tuesday after the team worked out Duke center Jahlil Okafor.
"We would like to bring in another player or two," Kupchak said. "[And] we'll revisit these players one more time in this building."
Lakers officials have already auditioned 54 prospects for their three picks in the June 25 draft. In addition to the No. 2 selection, they have Nos. 27 and 34.
Possibilities for their highest pick also include Ohio State's D'Angelo Russell; Emmanuel Mudiay, who played in China last season, and Kentucky's Karl-Anthony Towns, who the team has yet to audition.
The Lakers will also look at Latvian forward/center Kristaps Porzingis over the weekend in Las Vegas. It's unlikely the Lakers will get a chance to audition Spanish guard Mario Hezonja.
Kentucky center Willie Cauley-Stein and Duke forward Justise Winslow are other high-level draft prospects who have yet to visit the Lakers. The team has auditioned Murray State point guard Cameron Payne, who isn't likely to be around for the Lakers' 27th pick -- but would be a reach at No. 2.
Kupchak has previously indicated that the Lakers could move their pick in trade, although the price would be significant.
"I think we're getting a comfort level. We've scouted these players," Kupchak said Tuesday. "You think you know them but until you get them up close, until you interview them, put them through workouts, stand 10 feet away for an hour and a half and watch them work, that's when you get a good feel."
Okafor, Russell and Mudiay each had individual workouts with the team, instead of the Lakers' preferred three-on-three format.
"It's tough when you're doing ... solo workouts, that there's only so much you can do," Kupchak said. "Little did they know we have [assistant coach]
Each also went out to dinner with the basketball operations department and had separate dinner meetings with Coach Byron Scott and his staff.
"All three of the players are very polite, well-mannered -- hearty appetites, for sure -- mature kids," Kupchak said. "They're far more mature at [19 years old] than, say, I was or somebody else was 30 years ago at 19. It's impressive to be around them."
"Of course, they get good tutoring and good advice from their representatives and their families. It's rare when you have a bad meeting or dinner or social gathering," he continued. "Everybody gets a different take on a kid, and you can usually get a good feel after a couple of hours."
Kupchak also said that it's important not to be overly impressed by interviews and workouts. The Lakers have scouted each of the four main candidates for their pick multiple times over the last year, and, though still awaiting a visit from Towns, "our comfort level with the three players right now is very good," Kupchak said.
Ultimately, the choice will be made by Kupchak, who is empowered by the team's executive vice president, Jim Buss.
"It's going to be my decision, with the support of ownership," he said. "I'll talk to our scouts. Jimmy and I will talk. We talk every day. He'll give his opinion, but it's rare when we have varying opinions."
The No. 2 pick will be the highest of Kupchak's career, and the highest since the franchise selected
"At the end of the day, somebody has to be accountable and, for better or for worse, that would be me," Kupchak said.