Usually your graduate degree is meant to be more specific and technical than your undergrad that way you can advance your career by being in the smaller pool of candidates with more technical expertise. I wouldn’t pursue an engineering degree just to “broaden my background.” If you’re passionate about systems engineering and want to work as an industrial engineer/systems analyst then go to Cornell; it’s great for that. I agree with @bluebayou in going down the MBA route instead. An MBA amplifies your prior work experience with an analytical business background and can be leveraged to much better recruiting than jumping from healthcare to systems engineering back to healthcare. FWIW, I work @ a top pharma/biotech and when we recruit graduate levels applicants, we evaluate them on a very specific skill set that’s related to the position and how they’ve demonstrated that through their research/projects. Disjoint between your previous work experience, your graduate degree, and the current job you’re seeking will be a mess unless you’re trying to career switch.
If you still have time you should check out JHU’s MHA program. I think it’s much more catered to what you want, health administration, and it has much better placement/recruiting.
JHU MHA outcomes-
https://www.jhsph.edu/departments/health-policy-and-management/degree-programs/master-of-health-administration/student-achievement-rates.html
Here are the career outcomes for both programs. SystemsEng is very techy and non-healthcare. MPH is healthcare focused and sort of academia-centric.
Cornell Engineering outcomes-
http://www.engineering.cornell.edu/resources/career_services/students/statistics/upload/Systems-Engineering-report-3.pdf