Every day, they make up a new discipline. The Clarkson College Doctor of Education (EdD) in Interprofessional Leadership fosters the study of leadership through an interprofessional lens. Interprofessional leaders are in demand as our world becomes more complex and interconnected on a global scale. $941/credit x 52 https://www.clarksoncollege.edu/education-leadership/degree-options/doctor-of-education-in-interprofessional-leadership/ Kent State has a similar program with 20 more credits, but it costs nearly half the amount Clarkson charges. https://onlinedegrees.kent.edu/degrees/doctor-of-education-interprofessional-leadership
"Interprofessional" often means interdisciplinary health professions education. This could be more on-target than a generic education doctorate for a candidate in that world, while still having some advantage from broadness.
I feel like if you can't lead people of different but related disciplines, have you really learned leadership at all? I wonder if there are unique differences inherent in leading a group of related professionals versus leading a team where everyone has the same role.