A possible step by the FDA to address safety concerns in a new experimental drug law could limit drug companies wanting to fast-track unrelated and potentially groundbreaking medicines.

President Donald Trump enacted May 30 legislation known as “right to try,” which allows patients to pursue unapproved treatments without being subject to the Food and Drug Administration’s regulations. Supporters of the bill hailed it as a victory for patients, who should be able to explore any and all options to cure their ailments; opponents say it’s a move to skirt the FDA’s effective expanded access program, at the risk...