They face a challenging path to build around their star trio.

If he’s said it once, he’s said it a dozen times: Frank Vogel loves talking about getting players to “star in their roles.”

Back when the discourse was if the Lakers would ever find a third star, or if one of their other players would rise to be a foundational piece like LeBron James or Anthony Davis, Vogel stressed that the team didn’t need one as long as everyone played their part.

“We need guys like that to star in those roles if you’re going to have the ultimate success,” Vogel said during last season.

Now the Lakers have a third star, pulling the trigger on a trade for Russell Westbrook from Washington to give the Lakers a former MVP and a formidable trio of AllStar players. But with a thinned-out roster, rising salary and intensely competitive market for minimum contract-level players, finding new “star in their role” candidates will be a difficult task requiring more than a little luck and guile for GM Rob Pelinka and his front office.

While last postseason was disappointing for the Lakers’ supporting cast, waving farewell to longtime role players like Kyle Kuzma and Kentavious Caldwell-Pope will probably hurt at points this season, because it will be tough for the Lakers to find equivalent players to fill out the roster.

The Lakers find themselves in a large-scale roster rebuild, even though the pillars are well-established. Outside of James, Davis and Westbrook, only Marc Gasol ($2.7 million) is under contract for next season. And yet the Lakers have about $123.5 million in salary committed to those four players, with their star trio all on max deals. The NBA’s salary cap is about $112.4 million, meaning the Lakers have no money to spend on free agents except the deals they can get signing their own players back, or on exceptions.

Those high salary numbers also mean the Lakers can’t operate under a hard cap as they did last year. With the NBA’s hard cap figure set at about $143 million, the Lakers wouldn’t have space to fill out the 15-man roster on minimums, much less re-sign key players like Alex Caruso and Talen Horton-Tucker (who are priority targets, according to a person with knowledge of the team’s offseason goals). That means bringing in another big star like DeMar DeRozan or Kyle Lowry on a sign-and-trade is out, as is using the full midlevel exception (which the Lakers used last season to sign Montrezl Harrell for $9.7 million annually).

Some fans have fixated on the idea that the Lakers can send out Dennis Schröder, now made redundant by Westbrook, in a signand-trade to another team to recoup some assets. The biggest problem is that the deal would require Schröder’s consent. The 27-year-old German guard had strong hopes at the beginning of the offseason that he would return to the Lakers, according to a person with insight into his thinking; it might sting to involve himself in a sign-and-trade deal that would make the franchise better without him in the picture.

Schröder has also made no secret that he’s looked forward to going through free agency for the first time in his eight-year career, and it’s more straightforward for him to leave the Lakers for nothing and join a team with cap space, like New York or Chicago. The only exception would be if Schröder and a prospective team without cap space want to make a deal happen and need the Lakers’ help to seal it.

The Lakers can go above the cap to re-sign key pieces: Caruso is one of the team’s best perimeter defenders and has shown a knack for playing alongside James, and even though he could command more than $10 million annually on the market, the Lakers will be motivated to bring him back. The same goes for Horton-Tucker, who is just 20 and is now the best young piece remaining – the Lakers can match any offer he receives in restricted free agency. Both may spur competition for their services, but with limited alternatives, the Lakers will have a lot of incentive to hammer out deals to bring them back.

They could also bring back Markieff Morris, a 2020 title winner who didn’t have a great season last year, but who the Lakers can use to fill out the roster as a stretch big if he can find his shooting touch. Alfonzo McKinnie, who was little used last season, has a non-guaranteed deal worth $1.9 million that can add depth.

From there, it gets tricky – and expensive. The NBA luxury tax figure is $136.6 million, which the Lakers are guaranteed to surpass. Every dollar they spend above that amount adds to their tax bill, which is liable to make them one of the most costly rosters next season. They can use the mid-level exception which is just over $5 million, and then they can sign players to minimum contracts. Expect the team to keep roster spots open to perhaps pluck up someone from the buyout market next season, similar to how they acquired Andre Drummond last season.

One problem for the Lakers is that there will be a number of contenders looking for the same type of player: a minimum-level veteran who can shoot threes and defend. Those players will have their pick of Brooklyn, Philadelphia, Milwaukee and other likely contenders. Without more money to offer, the Lakers may have to dangle other kinds of incentives – like playing roles.

The Lakers added a pair of promising two-way players to their roster Thursday: Gonzaga’s Joel Ayayi and Oklahoma’s Austin Reaves. Both undrafted players could figure into playing mix if the roster winds up light, and it seems telling that both are mature players with lots of college experience.

It’ll be all hands on deck this coming fall, no matter who the Lakers are able to pull into the roster around James, Davis and Westbrook. And hang on through the next week – the seas might get a little choppy.