States that declared themselves refuges for transgender people have essentially issued an invitation: Get your gender-affirming health care here without fearing prosecution at home. Now that bans on such care for minors are taking effect around the country, patients and their families are testing clinics’ capacity. Already-long waiting lists are growing, yet there are only so many providers of gender-affirming care and only so many patients they can see in a day. For those refuge states — so far, California, Connecticut, Colorado, Illinois, Massachusetts, Maryland, Minnesota, New Jersey, New Mexico, New York, Oregon, Washington and Vermont, plus Washington, D.C. — the question is how to move beyond promises of legal protection and build a network to serve more patients.