“T-cells are very powerful,” said Dr. Campana, formerly of St. Jude and now at the National University of Singapore. “In the same way they can eliminate cancer, they can also kill you.”

A protein called HER2, for instance, is found on many breast and other tumors, making it a seemingly good target. But it is also found in tiny amounts in the lungs. When Dr. Rosenberg’s team infused killer T-cells aimed at HER2 into a patient, she went into respiratory distress within 15 minutes and died five days later.

The treatments work for the blood cancers because there is a good target. But finding these for the most common cancers has been difficult.

One problem is that CARs, because of how they are made, can bind only to proteins on the surface of cancer cells. But most proteins made by these cells, or by any cell for that matter, are inside the cell, out of reach.

There is an alternative approach that is gaining interest. Patients’ immune cells can be engineered to make what are called T-cell receptors, or TCRs. These can recognize proteins inside the cancer cells.

Some experts say TCRs, which have a far wider array of potential targets, represent the best hope of using cell therapy to treat solid tumors. There have been hints of effectiveness already in treating one of those, a type of sarcoma.

It might turn out that the best target for each patient will be unique to that person. Scientists are now experimenting with using DNA sequencing and other techniques to find the best mutated protein in each person’s tumor at which to aim the claw.