For years, fundraising efforts at Stuyvesant High School have lagged far behind those of its elite public-school peers, stymied in part by disorganization and infighting at three dueling alumni groups.

Now, a $1 million donation from hedge-fund manager Boaz Weinstein—which, when completed, will be the largest in the school's history—has revived hopes that the groups will merge into one organization that will put it on par with the city's other competitive high schools.

On...