Billionaire Carl Icahn bought 702,877 shares of Lionsgate this week, raising his stake in the movie and TV studio about 0.5% to 33.1%, he says in an SEC filing today. What appears to be his first purchase of the studio’s stock since July 2010 likely will lead company watchers to wonder whether he plans to make another move to take control — possibly at Lionsgate’s shareholders’ meeting in Toronto on Sept. 13. Icahn’s filing says nothing about his plans, just that he bought the stock in a range of $6.74-$6.90 a share. Lionsgate closed Friday at $7. But the timing is curious: The additional shares give him a bit more power if he wants to put directors he favors on the Lionsgate board. Icahn has said that the company’s been mismanaged and spends too much. He could offer other candidates for the board at any point up to the meeting. Last year, Icahn had five nominees, all of whom lost. Lionsgate said on Friday that it is running the same 12-director slate that was elected last year.