Cablevision Systems Corp. investor Mario Gabelli called for the founding Dolan family to break up the company, stepping up demands he made two days ago and threatening a proxy fight.

Mr. Gabelli’s proposal is more far-reaching than one he made two days ago, when Bethpage, N.Y.-based Cablevision said it would consider spinning off assets, buying back stock, and paying a dividend. The Dolans have come under criticism from Cablevision investors, who rejected their bid to buy the company for $36.26 a share last year.

Cablevision should sell its Rainbow Media unit of cable-TV networks, spin off Madison Square Garden, and explore a sale of its cable systems to Time Warner Cable Inc., Mr. Gabelli said yesterday in an interview with Bloomberg.

“They have made a commitment to follow through,” said Mr. Gabelli, who two days ago called on Cablevision to sell Rainbow and use the money to buy back stock. “If they don’t, there are board seats available.”

Cablevision rose 45 cents to $27.60 in New York Stock Exchange composite trading. It has gained 30% since the company said on July 31 it would seek ways to boost the price.

Mr. Gabelli predicted the company will do “something in between” a full breakup and his August 5 proposal. His Rye, N.Y.-based Gamco Investors Inc. owned 8.3% of Cablevision as of March 31.

A spokeswoman for Cablevision, Kim Kerns, declined to comment on Gabelli’s remarks.