“Our commitment to cancer will continue for the next generation at least,” Mr. Huntsman said. “With mental health, there were enough experiences in our own family that if we didn’t have the name or the wealth we wouldn’t have gotten nearly the care we got.”

He said a study showing that Utah ranked last for adult mental health care among the states and the District of Columbia accelerated the family’s donation to a mental health cause. He would consider the $150 million gift a success if people in Utah and the surrounding states began to look to the Huntsman Mental Health Institute for care, the way they do with the cancer center.

“When we think about mental health longer term, we will have succeeded if a single mother in rural Nevada or Idaho has a teenage child they’re worried about and they come to us,” he said. “The real result will be: Is the world going to be any different for that single parent? Or is real psychiatric health the domain of the rich and powerful? If that’s the case, then we’ve really lost the battle.”

While he has taken the lead among his eight surviving siblings, Mr. Huntsman said they were very much involved. Their opinions on philanthropy also sometimes differ from their father’s approach.

Mr. Monnier said the next generation must determine its path : “Do we want to do what Dad did, or do we want to do our own thing?”

The risk in just following parents’ lead, he said, is that family members won’t be engaged and will feel as if they’re being controlled from the grave, as it were.

After the 1988 earthquake in Armenia, for example, Jon Huntsman Sr. said he was moved by what he had seen on television and began donating to aid groups there. He eventually gave more than $50 million to help rebuild the country’s infrastructure. He also gave scholarships to bring Armenian students to the United States to study.