When Nick Perrino introduced pizza to the Home Run Inn tavern on Chicago’s South Side in 1947, he laid the foundation for a business his children would later inherit.

Today, it’s more than a pizza joint.

Joe Perrino,

Nick’s son and the chief executive officer of Home Run Inn Inc., oversees nine pizzerias in the Chicago area, a frozen food division, a frozen food distribution partnership and a real-estate business.

When second- and third-generation managers take over the family business, they often face more complex issues than their parents once did. Owners like Mr. Perrino are now fueling a rising demand among business schools for programs that cater to their specific needs in areas such as succession planning, asset management and communication.

Columbia Business School in 2012 brought in an executive-in-residence and added a course on family enterprises and wealth; enrollment in the course nearly doubled to 47 students last year, according to the school. The University of North Carolina’s Kenan-Flagler Business School has also seen rising demand for its two courses on family business, officials say. Next year, Cornell University’s Johnson Graduate School of Management plans to open a family-business program offering coursework and a speaker series for students and executives.

“The demand is there in the marketplace; we see the demand from students, so I think it’s only healthy that professors from the elite schools are excited to work in this area,” said Johnson Dean

Soumitra Dutta.

Mr. Perrino and several of his family members have taken courses at Loyola University Chicago’s Quinlan School of Business. The Home Run Inn chief executive also asked his son-in-law,

Sean Bolger,

the company’s vice president of real estate, to register at Loyola’s family business center, which offers continuing education to family business operators and their employees.

“It expands your level of knowledge of a family business from a business aspect, family aspect and on the leadership front,” said Mr. Bolger, who has completed one of the two classes offered by Loyola’s family business center.

Mr. Perrino said his father didn’t prepare his family for his exit from the company before he died. His father hadn’t talked to Mr. Perrino or his sisters about the roles they would have once he died, he recalled.

“It taught me, at the time of his death, to really proactively work on communication and involve the family in at least the information part of the business,” Mr. Perrino said.

Loyola caps its two classes for business owners and employees at 12 people per 18-month class. Waiting lists for the programs, one that teaches family business basics and one that is specifically designed to prepare future leaders, have filled up quickly over the past few years, said

Andrew Keyt,

director of Loyola’s family business center.

Family businesses aren’t always small. Large employers like Enterprise Holdings Inc., which owns brands like Alamo Rent A Car, Enterprise Rent-A-Car and National Car Rental; household-products company SC Johnson & Son Inc. and Mars Inc., the maker of M&M’s, continue to be family-owned. And they require predictably different skills than other businesses, particularly when it comes to social dynamics, management professors say.

“The issues that are related to family-owned businesses can be so unique, complex, and multidisciplinary that I can’t imagine getting an M.B.A. without being exposed to them,” said

Patricia Angus,

a family wealth consultant who teaches the course on family enterprises at Columbia Business School.

Because family businesses exist in the “intersection between personal and professional life,” said Prof. Angus, her course touches on a wide range of topics, including governance, family systems and philanthropy.

Write to Adam Rubenfire at Adam.Rubenfire@wsj.com