A group of business leaders—including Ben Cohen and Jerry Greenfield of Ben & Jerry's ice cream and former Nirvana manager Danny Goldberg—are planning to pour substantial funds into the Occupy Wall Street movement in hopes of sustaining the protests and fostering political change.

Their goal is to provide some ballast to an amorphous movement that captured the world's attention with nonstop, overnight protests in dozens of cities but has had trouble regaining momentum since...