Aletta Collins is telling me about what arrived in the post when she started her latest project. “A big parcel came and it was my vocal score for West Side Story,” she says. “But then there was this other score,” she mimes holding a weighty tome. “And I opened it and it was the choreography, this most beautiful book with absolutely every movement all written out and diagrams, so detailed and exact. Because everybody who does West Side Story uses the same choreography.” Or at least they did, until now.

Since its stage premiere in 1957, Leonard Bernstein’s score for West Side Story has been inseparable from Jerome Robbins’ choreography, a masterful marriage of movement, music, character and narrative. Robbins also directed the musical (and the 1961 film version) and his iconic moves defined the rivalry between the Jets and the Sharks, his mid-century jazz-ballet never losing its cool.

But change is afoot, because a clutch of new West Side Stories are wiping clean the choreographic slate. Avant-garde director Ivo van Hove is creating a new Broadway production with Belgian choreographer Anne Teresa De Keersmaeker, set to preview in December. And there’s a Steven Spielberg movie in the works, with New York City Ballet choreographer Justin Peck on board. But before either of those comes a new production at Manchester’s Royal Exchange Theatre, directed by Sarah Frankcom, which faces Collins with the challenge of being the first choreographer in a major professional production to rewrite Robbins’ steps.

It’s a radical act. “The way [the original] shaped choreography, let alone musical theatre, it’s in the fabric of one’s being,” says Collins. “I told a friend I was doing it and they said they’d never seen West Side Story. I said, I bet you can impersonate how they dance. And he went, ‘Is it something like this?’” she leans forward in her seat and clicks her fingers in true Jets style. “That’s how far-reaching it is.”

Collins isn’t out to rebel against Robbins for the sake of it. In a rehearsal studio at the Royal Exchange, I watch a run-through of a scene where the two gangs face each other down at the gym. The room is bursting with energy, with elements of Latin, street dance and northern soul all coming through in the choreography. The dancing feels vibrantly alive and looks different to the original while definitely sharing some of its spirit. “It’s still two groups of people threatening each other with knives over doing a mambo,” says Collins. “It’s going to start in a fairly similar place.”

“I think all great pieces of work need to be reimagined,” says Frankcom. “Jerome Robbins was saying something about where dance was at that time. The relationship between dance and theatre is really different in 2019.”

Collins has a background in contemporary dance but now works as a choreographer and director across dance, theatre (The Hairy Ape, The Twilight Zone) and opera (Coraline), and her approach certainly reflects the way most choreographers work today, in collaboration with their performers.

She describes the way she develops movement in the number Cool: “It starts in the drugstore, with the Jets waiting for the Sharks to arrive for this war council. Riff, the leader of the Jets, is telling them all to be cool. So the image we had of him was of a chef with all these saucepans, ready to blow, having to keep the lid on it all. We started looking at movement where you’re trying to keep the lid on your own dynamics, working with the adrenaline of fight or flight. I got them to create their own gestures to show what it’s like to try to sit still when all you want to do is express this huge amount of energy.”

Collins is not a choreographer with a set style, but aims “to try to find something that comes out of character and location” – in this case, the competition for space in the city between first- and second-generation immigrants. The era of Frankcom’s setting is deliberately unspecific, but she sees clear parallels with today. “This could not be more relevant in terms of the potential of young people, the knife crime happening on our streets, the notion of difference and how living alongside people can actually be really difficult. The material felt very fresh.”

Collins is approaching the project with “a healthy balance between trepidation and excitement”, admitting that the Robbins version is “perfect – there’s nothing about it where you don’t go: ‘Wow, that’s beautiful.’”

But nevertheless, she has found it liberating being freed from the sacred choreographic score. Will her friend recognise it as the West Side Story of his imagination? “Well,” she laughs, “it does have some finger clicks,” she says. “But maybe I’ve put them in different places.”

• West Side Story is at the Royal Exchange, Manchester, until 25 May