Patients with metastatic cancers are generally denied organ transplants, even if they are in remission, because the high chance of relapse means the organs would very likely be “wasted.” Ms. Zak’s doctors at Cleveland Clinic say she should be granted an exception because she was treated with a new immunotherapy that may well keep her in permanent remission . Her insurer has been persuaded by this argument, but UNOS appears not to have been. Ms. Zak’s doctors have petitioned the network four times for an exception — so far, to no avail.

A spokesman for UNOS stresses that the organization is doing its best to ensure that organs get to the people who need them most but that it is trying to manage a great shortage of a very precious resource.

UNOS, indeed, is in an awful position, forced to make life-or-death choices every day.

Far too few people are donating organs to begin with, and far too few of the organs that have been donated are making their way to patients in waiting. Experts say that misconceptions about donor eligibility requirements and, in some states, cumbersome registration processes are preventing nearly half of those who support organ donation from becoming registered donors. Outdated standards are causing transplant surgeons to reject some 75,000 usable organs every year, according to a Washington Post analysis. And an astounding lack of accountability and oversight in the nation’s creaking, monopolistic organ transplant system is allowing hundreds of thousands of potential organ donations to fall through the cracks.

In July, President Trump ordered the Department of Health and Human Services to devise stricter rules for the nation’s transplant industry. That’s a welcome call for change — one the health secretary, Alex Azar, should heed quickly and thoroughly. But on their own, such measures will not repair the nation’s organ donation system. The following steps are also needed:

Fix the UNOS scoring system. This year, UNOS made several changes to the way it “scores” potential organ recipients. The network says the changes were meant to make organ distributions more fair. But as Ms. Zak’s case demonstrates, they have made at least some decisions more arbitrary. Her final score was determined not by her doctors’ careful evaluations, but by an anonymous panel of five transplant professionals who reviewed a short application — rather than Ms. Zak’s full medical records. An UNOS spokesman says that the criteria used in such scoring decisions were created in consultation with the transplant community and that a patient’s score is not the only thing that determines whether or not she receives an organ.

Revisit the UNOS monopoly. The federal contract that grants control of the nation’s organ procurement system is valued at nearly $58 million per year. Because most of that money comes from patient fees, there is more of an incentive to add patients to the wait list than to secure organs for them. UNOS has held the contract exclusively for more than 30 years, during which time the nation’s organ shortage has risen steadily. Critics of the network say that a lack of competition has thwarted innovation, allowed the organization to become mired in bureaucracy and made it resistant to change. Other groups have expressed interest in bidding against UNOS, but the government agency responsible for the contract has done little to encourage those bids. UNOS says that few organizations could match its expertise.