Formal mentorship is currently supported by philanthropy and federal agencies including the Office of Juvenile Justice and Delinquency Prevention and the Corporation for National and Community Service. In the fiscal year 2015, OJJDP granted $90 million to mentoring organizations to support at-risk youth across the country—a sum sufficient to cover hundreds of thousands of students but not sufficient for need, according to Shapiro.

But other limitations, beyond funding challenges, make it difficult to expand such programs. For one, mentorship programs aren’t always effective. (In some cases they can even prove harmful, particularly when it comes to mentoring relationships that terminate prematurely.) For another, a prevailing thread among education experts today is that a single mentor isn’t sufficient. “We’re too enamored with the idea of the heroic volunteer who swoops in,” said Marc Freedman, the author of the influential 1999 book, The Kindness of Strangers: Adult Mentors, Urban Youth, and the New Volunteerism.

Indeed, education experts and nonprofits are embracing the idea that a broad web of formal and informal mentors is key to successfully serving young people. “This changes the conversation from ‘You have to be everyone to someone,’ to ‘You have to be someone to everyone,’” said Jonathan Zaff, the executive director of the Center for Promise, echoing an argument recently put forth by the Harvard political scientist Robert Putnam in his book Our Kids: The American Dream in Crisis. In an email, Putnam, who in his book notes that privileged youth are two to three times more likely to have an informal mentor outside of their family, said that “kids from working-class homes need more caring adults in their lives.” Disadvantaged students, he said, often lack access to the range of role models available to their more privileged peers—such as coaches, clergy, neighbors, or family friends. Absent these advisors, underprivileged students may be deprived of the kinds of information necessary for navigating and thriving in large institutions like colleges—for exercising what Putnam described as “savvy.”

Mandy Savitz-Romer, a senior lecturer at Harvard’s Graduate School of Education, cited a difference in perceptions of the future between privileged students and their counterparts, many of whom are at a major disadvantage because they do not believe they are “post-secondary material.” Adults, she observed, need to help underprivileged students believe that they can go to college. “The idea that you have a future in higher education does not exist,” she said of some communities.

Mentors are just one form of role models on campus that can shape student outcomes. School counselors represent another tier of non-teacher adults who can make a large difference for students: A 2013 study correlated the addition of a single guidance counselor at a given school with a 10 percentage point increase in four-year-college-going rates at the school. Still, like mentorship programs, school counseling suffers from limited funding.