Ms. van Ewijk wanted her children to be full siblings, so she still wanted Mr. Meijer to be the donor. Nonetheless, she was alarmed. The Netherlands is a small country, home to 17 million people; the more half siblings there are in the population who are unknown to one another, the greater the odds that two of them might meet unwittingly and produce children of their own — children with a heightened risk of carrying hereditary defects.

Furious, Ms. van Ewijk confronted Mr. Meijer. He admitted that he had produced at least 175 children and conceded that there might be more.

“He said, ‘I’m just helping women make their biggest wish come true,’” Ms. van Ewijk recalled. “I said: ‘You’re not helping anymore! How do I tell my kids that they could possibly have 300 siblings?’”

She may have only known the half of it.