Amid building anger over a sluggish European Union coronavirus vaccine rollout that has left them far behind several other wealthy countries, many E.U. states are looking beyond the bloc’s joint purchasing strategy, which now seems woefully underwhelming.

An immense black — or at least gray — market has arisen, with pitches from around the world at often exorbitant prices. Sellers have approached E.U. governments claiming to offer 460 million doses of vaccines, according to the early results of an investigation by the bloc’s anti-fraud agency that were shared with The New York Times.

While they still plan to get vaccines from the bloc, some nations are also trying to negotiate directly with drug makers and eyeing the murky open market where they are still unsure of the sellers and the products. Some have also agreed to swap vaccines with each other, deals some of them now have reason to regret.