SSince June, when billionaire activist investor Paul Singer’s hedge fund first announced it had acquired a $1.9 billion stake in Southwest Airlines, the Dallas-based airline has made many concessions in its effort to stave off a coup.

In July, Southwest announced it would eliminate open seat selection and switch to reserved seats instead – a key proposal made in a 51-page presentation to the airline’s board by Singer’s Elliott Investment Management. The hedge fund responded that the changes were “too little, too late.”

Earlier this month, Southwest gave in to further demands from Elliott when CEO Gary Kelly and six other Southwest board members announced their resignations.

Elliott said he was “delighted” with the offer, adding: “In our experience, this is unprecedented.”

But that’s apparently not enough. On Tuesday – two days before Southwest’s investor day, where the airline is expected to unveil further changes to its business model – the hedge fund announced that it would call a special meeting at Southwest Airlines “in the coming weeks.”

“We do not support the company’s current course, which is being haphazardly pursued by a group of executives in pure self-preservation mode,” Elliott partner John Pike and portfolio manager Bobby Xu wrote in a letter to shareholders.

The letter accuses Southwest’s leadership of trying to prevent a leadership change through “a chaotic series of defensive measures, including a ‘poison pill,’ the hasty hiring of a new director, a half-hearted announcement of changes to the company’s product, and the sudden declaration that nearly half of the board plans to resign in November. CEO Gary Kelly has also stated that he plans to resign, but not until next May.”

“It is unfortunate that Elliott not only completely failed to engage constructively, but today continued his pattern of public attacks and attempted to disrupt Southwest’s upcoming Investor Day,” the airline responded in a statement.

This kind of controversial back-and-forth is not uncommon when a company is in the crosshairs of an activist investor.

“I think Elliott wanted to make it clear that we’re still here,” said Keith Gottfried, CEO of Gottfried Shareholder Advisory, a shareholder activism defense firm, adding that the letter to shareholders was a way for the hedge fund to exert its influence ahead of Southwest’s presentation on Thursday. “It will be a webcast, and I’m sure there’s a script being finalized. And I think Elliott wants to have some influence. Whether it’s big or not, we don’t know, but it’s hard to believe he won’t have influence on the script that’s presented tomorrow.”

Southwest’s board has consistently supported CEO Bob Jordan, but Elliott has made it clear he wants him out. The hedge fund has proposed 10 possible candidates for the airline’s board and could use the special meeting to elect them.

“Before Elliott had even spoken to CEO Bob Jordan or heard of the company’s plans, he had already made his position clear in advance and was adamant about his demand for a two-thirds majority on the board and an immediate CEO change,” Southwest said.

Last week, Bloomberg reported The Southwest Chief Operating Officer Andrew Watterson told employees to prepare for “more difficult decisions” as the airline tries to fend off Elliott’s demands.

Elliott rejected that portrayal. “To be clear, whatever ‘difficult decisions’ management had to make were the product of a failed management team that has performed worse for years and is now taking any short-sighted action it believes will save its own jobs,” Pike and Xu wrote. “Elliott had no say in any of those actions.”

southwest Investor Day The presentation begins at 10:30 a.m. Eastern time on Thursday. Gottfried will look for signs that Southwest is responding to Elliott.‘s ongoing concerns. “One goal would be to take a step back, take the kettle off the stove,” he says.

Shortly after the market opened Wednesday morning, Southwest shares were trading at $30.16, up slightly from where they were before Elliott’s announcement on Tuesday. The company’s shares have risen about 10 percent over the past year, while the benchmark S&P passenger airline index has gained 17 percent over the same period.