Southwest Airlines' battle with activist investor heats up: Are free bags on the chopping block?

Activist investor Elliott Investment Management has continued pushing for a "comprehensive" review of Southwest Airlines' business while building its stake in the carrier.

Elliott now holds 10% of the airline’s common stock, a Tuesday filing with the Securities and Exchange Commission (SEC) showed, allowing it to call a special meeting with Southwest.

The investment firm has also advocated for numerous changes at Southwest that it has argued will improve the carrier’s financial performance. As part of Elliott's push for a business review, it said the airline has "written off key commercial innovations and revenue opportunities across the airline industry" in the past, like checked bag fees.

The luggage policy at Southwest allows customers two free checked bags, regardless of the type of ticket fare.

"There’s no work currently underway to change our industry-leading two bags fly free policy, but it’s important for us to know what our Customers value most," Southwest said in a statement to FOX Business. "We’ll continue our efforts to track stakeholder sentiment on many aspects of our business model to ensure we remain competitive and current on Customer preferences."

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The airline has been facing an activist investor challenge from Elliott since June. Representatives from both the airline and the investment firm are meeting early next week.

"We remain prepared to meet with Elliott next week and look forward to sharing details on our continued transformation at our Investor Day on Sept. 26," Southwest told FOX Business.

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The company has previously said it plans to "provide more details on its comprehensive plan to deliver transformational commercial initiatives, improved operational efficiency and capital allocation discipline during its Investor Day in late September."

There have been some new policies announced for Southwest customers in recent months.

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In late July, Southwest said it would start assigning seats and offering premium seating options on all flights in the future, a departure from its open seating and all-economy-class cabin, as FOX Business previously reported.

FOX Business' Daniella Genovese contributed to this report.