Mark Rylance to star in "Dr. Semmelweis" on the West End this summer. Could Broadway be next?

Sonia Friedman and the National Theatre are producing it at the Harold Pinter Theatre beginning June 29. Tom Morris is directing, and Stephen Brown co-wrote the play alongside Rylance. It's been 5 years since Rylance was last on Broadway (Farinelli and the King), so if this is well-received it would seem like an apt vehicle for his return, perhaps as early as winter/spring 2024.

Here's the copy from the show website:

Mark Rylance returns to the West End as one of medicine’s greatest pioneers, maverick Hungarian doctor Ignaz Semmelweis – the man whose research could save many millions of mothers’ lives.

But what good is a discovery that is ignored?

In Vienna, a city of artistic and scientific revolution, thousands of women are still dying in childbirth each and every year. Only Dr Semmelweis can see the invisible killer at work, but to stop it, he must convince his colleagues to admit culpability and approve change.

Damned by an establishment that questions his methods, his motives and even his sanity, Semmelweis is haunted by the women he has failed to save. Can he finally convince the greatest doctors of 19th century Europe to accept his argument – and what will it cost him to make an almost impossible case?

Following a “smash hit” (Mail on Sunday), sold-out run at Bristol Old Vic, this “compelling new drama” (The Telegraph) directed by Tom Morris, featuring live music by Adrian Sutton and original choreography by Antonia Franceschi of Balanchine’s New York City Ballet, comes to the Harold Pinter Theatre in the West End for a strictly limited run this summer.

I’m in London over the summer and did some research on this production as a potential option. From what I found, the reviews were quite middling when this production (with Rylance) was first produced.