LAWRENCE — The offseason Kansas basketball has had to date has made headlines, and for good reason.

Although Kevin McCullar Jr. and Johnny Furphy are headed to the professional ranks and the NBA draft, a trio of veterans — KJ Adams Jr., Hunter Dickinson and Dajuan Harris Jr. — have all elected to return to college. Through the transfer portal, coach Bill Self and company have added high-profile talents such as Zeke Mayo, AJ Storr and Rylan Griffen. Even a pair of freshmen, Flory Bidunga and Rakease Passmore, are already turning heads.

But all of that doesn’t mean Self and his staff are done adding to their roster. As they look to challenge for more Big 12 Conference and national success, after struggling more than they anticipated last season, efforts are underway to bolster their depth. The timeline for how long that will take is unclear, but they aren’t sitting idly by.

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“I would like to have, I think, one more, in a perfect world, but I think we’re better,” Self said. “We obviously have a little bit more depth on paper and — but last year at this time we had more depth, too. So, unexpected things can obviously happen. But, yeah, I like our roster a lot. We were fortunate to get KJ and (Harris) and (Dickinson) to all come back.”

What would be ideal, from Self’s perspective, is to have eight guys he could consider as bonafide starters when they tip off the 2024-25 campaign. That would give Kansas a bench that would be much deeper than it was last season. But it’s not as if the next person the Jayhawks add to their roster has to be someone who would come in and start for them.

Sure, Self acknowledged, adding another starting-caliber talent would be nice. But he also highlighted a need to bring in someone who can, in their role, help make everyone else better and not necessarily be the one who scores a ton of points. Pointing to past KU players, Self mentioned the likes of Tyrel Reed, Brady Morningstar, Travis Releford and Kevin Young.

Self, who left the door open to the addition being an international prospect, appeared to push back on the notion that it would be tough to find someone who would be willing to come in and fill that type of role for Kansas. When it comes to the portal, he mused that people enter it with different objectives. Self said some think about name, image and likeness (NIL), some about looking to go somewhere and win, some about searching for a more significant role and some about wanting to be a part of a certain program.

“We’re talking to some guys,” Self said. “So, hopefully we can find someone that fits with what we’re trying to do and will fit and compliment the guys we already have.”

As long as everyone remains healthy, that next addition to the roster could be more of a luxury than anything else. But last season also showed relying on that can be a bit of a gamble. Even this week, during a scrimmage with current players at a local camp, Elmarko Jackson — a freshman last season — experienced a hard fall near the basket and his leg was evaluated on the court as the scrimmage ended.

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Self told the crowd of children at the camp Jackson was all right. With some assistance, Jackson did eventually walk off the court. But the moment showcased how quickly something can change, even before games have been played.

“Obviously I saw the fall, but I didn’t really see what happened because I was on the bench,” Dickinson said. “But it was good to see him being able to walk it off on his own and under his own strength, relatively. So, hoping for the best. I’m not sure, but we’ve got a really good training staff that’ll get him back as soon as he can.”

Jordan Guskey covers University of Kansas Athletics at The Topeka Capital-Journal. He is the National Sports Media Association’s sportswriter of the year for the state of Kansas for 2022. Contact him at jmguskey@gannett.com or on Twitter at @JordanGuskey.

This article originally appeared on Topeka Capital-Journal: Who will Kansas basketball coach Bill Self add to Jayhawks' roster?