Billionaire Kirk Kerkorian’s Tracinda Corp. investment firm says it has purchased an additional 20 million shares of Ford Motor Co. at $8.50 per share.

In a filing with the Securities and Exchange Commission today, Tracinda says it now owns 140.8 million shares of Ford stock, increasing its stake in the auto maker from 5.5% to 6.49%.

The investment firm also says it may propose strategies for Ford and has explored a capital infusion to aid the auto maker in its restructuring.

The move comes after a June 17 meeting between Ford CEO Alan Mulally, Executive Chairman Bill Ford and officials from Tracinda, including Kerkorian.

Ford says in a statement the meeting was “positive” and a “chance for the leaders of both companies to discuss elements of Ford’s transformation plan that we have announced publicly.”

Tracinda began buying Ford shares April 2 and repeatedly has said its interest in the auto maker is due to its strong performance during difficult economic conditions.

On Wednesday, Ford shares fell 5.8 % to $6.22 but opened today up $0.10 to $6.32.