Several major hospital systems, including Ascension, a Catholic system that is the nation’s largest nonprofit hospital group, plan to form a new nonprofit company, that will provide a number of generic drugs to the hospitals. The Department of Veterans Affairs is also expressing interest in participating.

In all, about 300 hospitals are now included in the group. Other hospitals are expected to join.

Dr. Harrison said they planned to focus only on certain drugs. “There are individual places where there are problems,” he said. “We are not indicting an entire industry.”

Dr. Kevin A. Schulman, a professor of medicine at the Duke University School of Medicine who has studied the generic drug market and is advising the effort, said: “If they all agree to buy enough to sustain this effort, you will have a huge threat to people that are trying to manipulate the generic drug market. They will want to think twice.”

The idea is to directly challenge the host of industry players who have capitalized on certain markets, buying up monopolies of old, off-patent drugs and then sharply raising prices, stoking public outrage and prompting a series of Congressional hearings and federal investigations. The most notorious example is of Martin Shkreli, the former hedge fund manager who raised the price of a decades-old drug, Daraprim, to $750 a tablet in 2015, from $13.50.

Hospitals have also struggled to deal with shortages of hundreds of vital drugs over the past decade, ranging from injectable morphine to sodium bicarbonate (the medical form of baking soda), shortfalls that are exacerbated when only one or two manufacturers make the product.