Just over a year from now, the Affordable Care Act is set to unleash enormous change in the health-care sector, and Cleveland Clinic Chief Executive Delos "Toby" Cosgrove is preparing his institution by expanding its reach and striving to make caregivers more cost-conscious.

The nonprofit has grown steadily since Dr. Cosgrove, a heart surgeon, took over in 2004 and now includes eight hospitals in Ohio along with its flagship campus and facilities in Florida, Las Vegas and Toronto. It's also helping to build a new hospital...