That work, “Harbor Me,” which had its premiere last year at Paris’ Théâtre du Châtelet, was created by Sidi Larbi Cherkaoui, a Belgian-born dancemaker with a Flemish mother and Moroccan father. Cherkaoui, who was appointed artistic director of Royal Ballet of Flanders last year, knows what it is to be the Other. He also knows how to get audiences thinking, feeling and questioning the status quo.

Set to a dark and mournful score—the stringed music of Korean composer Woojae Park’s “Extension” (in three aptly named parts: “Abyss,” “Morphosis” and “Be Adrift”)—the 20-minute opus was originally made for a trio of men. On Friday night, Aaron Carr, Morgan Lugo and Robbie Moore took center stage in this auspicious, Olympian undertaking, the level of virtuosity a 10 and the degree of dedication surpassing that, with a kind of divine humanity at stake.

Indeed, Cherkaoui’s ruminations on movement, whether a fluid, easy vocabulary or one that accesses struggles—finding shelter or offering same—not only speaks to, but pierces the heart and soul of dance. He also doesn’t shy away from asking the big questions: Do humans have the instinct to protect each other or, conversely, are they prone to destroying one another? And by likening us to elements—fire, water and air—emblems that scorch, douse and buffet one another to the point of no return, the conundrum persists.

Punctuated by extraordinary lifts, with trust underlying each coupling, thus tilting towards hope as opposed to destruction, the work tattooed itself onto the brain. A droning bass line served as a sort of anchor, with the threesome rolling and pitching—balancing on necks then collapsing into splits or cartwheels—this oceanic metaphor of coming unmoored, extended as well, to always-moving tides, a source of never ending mystery.

In a show of brute strength, the men also assayed a series of dynamic shoulder stands and spins, releases and unions, the longing for connection omnipresent. This was an action painting come to life, but not a Pollock: Cherkaoui has fabricated a Renaissance masterpiece—think Botticelli or Donatello—with the men bathed in Fabiana Piccioli’s dark but sumptuous lighting design, an occasional golden aura recalling Rembrandt’s use of light.

With outstretched arms at times in crucifixion pose, dancers also brought to mind the holy trinity, as Piccioli’s visual concept, a backdrop of billowing silk, proved the perfect complement to this cerebral, yet visceral, voyage.

Here, too, was shape-shifting at its best, no matter that relationships veered between harmonious and quasi-Machiavellian, the performers’ limbs alternating between Krishna-like and beckoning. Bits of Bharata Natyam could also be seen, as Park’s otherworldly score, which made use of a Korean harp as well as the geomungo, a six-stringed Korean zither, at times paralleling the dancers’ supple bodies, with the composer incorporating both plucking and bowing sounds that, onstage, manifested themselves as a sort of corporeal yin and yang.

And while the testosterone-fueled yang was out in full force Friday, the huge news was that “Harbor Me” would be performed by a female trio on Saturday. To quote Diaghilev’s pet phrase, “Astonish me,” this reviewer and those lucky enough to attend both performances, were duly—and doubly—astonished.

It is, after all, the rare choreographer who makes a work for one sex, then, at a later date, has the opposite sex perform same. (Batsheva’s Ohad Naharin did this with “Project 5,” where he chose to go from female to males in the work’s “Black Milk” section.)

That said, Stephanie Amurao, Julia Eichten and Lilja Rúriksdóttir could not help but give their performance a completely different spin. Talk about being gender fluid! Seriously, the women demonstrated fierceness that the dance demanded, but with the added measure of having a free-floating softness that was endemic to their XX chromosomes.

A sadness, decidedly, prevailed, though the gals’ lifts appeared more loving than those of the men, the latter, by nature, skewed to he-mannish and muscle-driven.

Yes, there was power, but in a sinewy, feminine form. The handstand-into-splits move and turns were almost—dare we say—mystical. This triad, too, engaged in a group struggle, but with their sea-of-sorrow motif also emanating from their bodies, as the women seemed more protected, more cosseted, more nurturing.

The dance, in effect, was something completely new—as if cast under a magician’s wand. The religious theme was still here, with Rúriksdóttir, a blonde from Iceland new to the company, spreading her arms, reminiscent not as a gesture of supplication, but as if one welcoming the world.

This harbor was a safe haven, with elastic moments of tenderness ritualistic in feel, the struggle to stay alive, against all odds, finally and firmly conquered through a shared spirit. Female power rocked, ruled and ran rampant in unexpected, yet very controlled ways, revealing the secret of life under Piccioli’s amber waves of light.

Both evenings were bookended by previously seen works: Justin Peck’s “Murder Ballades,” a jaunty dance from 2013, again featured six dancers successfully gamboling in sneakers to the raucous sounds of Bryce Dessner, offering unbridled joy in the process; and Millepied’s “Hearts and Arrows” (2014), performed to Philip Glass’ String Quartet No. 3 (“Mishima”). Eight dancers, deployed to great effect, shone with pinwheel-ready arms, gymnastic gyrations and dazzling spins. Completing the roster of terpsichores on both nights: a buoyant Anthony Bryant, the brilliant and agile Nathan Makolandra, and the redoubtable Rachelle Rafailedes.

Since its inception, L.A. Dance Project has been fortunate to tour the world, traveling to more than 11 countries and 34 cities, including performing in the Palace of Versailles. It was terrific, then, to see the troupe on its titular home turf, making this journo/dance junkie excited that LADP will be dancing again locally—at the Hammer Museum, February 20, and again on April 12, 15-17, 21-24. Welcome back, oh marvelous movers and shakers!