A company that was created through a spin-off is now proposing a spin-off of its own: The Madison Square Garden Company, the owner of the New York Knicks, New York Rangers and New York Liberty, wants to separate its professional sports teams and cable networks from the management of live events associated with the popular Gotham landmark that gives the company its name.

The company said it could not guarantee it would proceed with the plan, but it intends to explore the notion of coupling the event-management businesses associated with its operation of Madison Square Garden. the Beacon Theater and Radio City Music Hall and separating them from its sports teams, regional sports cable outlets and stake in SiTV, which operates the Fuse and Nuvo TV entertainment networks.

The proposal would further splinter an operation that was once part of Cablevision Systems, the cable-distribution-and-entertainment company controlled by the Dolan family. Madison Square Garden was spun off from Cablevision in 2010. In 2014, it made itself smaller by selling off its Fuse music-TV network to SiTV Media, a company that has in the past sought out young Latino audiences.

“Investors favor companies with greater strategic focus on their core businesses. We are exploring the opportunity to improve upon the excellent shareholder return created since MSG’s spin-off over four years ago by separating our business into two companies, each with its own distinct value proposition for investors,” said Tad Smith, the company’s chief executive, in a prepared statement.

The company did not set a timetable for completion of the process.