It seemed like an unbeatable formula: a brilliant concept, dazzling designs, rave reviews and a plan to share the costs. Stefan Herheim’s acclaimed staging of Wagner’s “Die Meistersinger von Nürnberg,” which wowed audiences at the Salzburg Festival in 2013, was headed to the Metropolitan Opera.

But on the road from Austria to New York, things hit a snag in Milan.

For that, you can thank the impossibility of creating one-size-fits-all sets for the world’s leading opera houses, muddled administrative leadership and a strained friendship. While the opera world is now flatter than ever, because of the growing number of global coproductions, taking shows on the road is rarely simple.

Coproductions are increasingly how leading opera houses do business, allowing them to share costs while presenting their audiences with a steady stream of shows that are new to them, even if not new to the world.

“In the old days, it was a badge of honor to have the premiere and have the production uniquely in your theater,” said Peter Gelb, the general manager of the Met, who has increased the company’s annual number of new productions, many of them coproductions. “And I think that has evolved over the years for economic reasons. But from my perspective, it’s not just economic. I’d rather be better than first.”