Carl C. Icahn boosted his stake in TWA to 31.6%.

In a filing with the Securities and Exchange Commission, the financier said his group purchased an additional 1.86 million shares of Trans World Airlines stock for $34.3 million on Thursday, lifting its holdings to 10.85 million shares. Before the latest purchases, Icahn controlled 26.2% of the airline’s stock. He has offered to acquire the airline by paying $18 a share for the stock he does not own. Based on the filing with the SEC, Icahn paid between $18.375 and $18.50 a share for his latest stock purchase.