What happened

Shares of Shake Shack (SHAK -1.68%) were climbing today on reports that an activist is circling around the fast-casual burger chain and planning a proxy battle for three board seats.

The restaurant stock closed up 7.8% on the news.

So what

According to The Wall Street Journal, Engaged Capital has been in talks with Shake Shack management for more than six months, and proposed to install new directors and make other changes that it thinks would boost the stock price.

The two sides appear to be at an impasse, and Shake Shack said in a statement that it is making financial progress on its strategic plan.

Engaged's nominees include Kevin Reddy, a former CEO of Noodles & Co; Joel Bines, who previously led the retail practice at consulting firm AlixPartners; and Engaged's co-Founder Christopher Hetrick. 

Engaged also said it has a plan to double Shake Shack's profitability in the next two years by making changes to its real estate strategy, store design, labor planning, and supply chain. Additionally, it aims to eliminate the company's staggered board, which means that shareholders vote for different board members at different times.

Now what

The response from the market shows that investors seem to agree that Shake Shack could use a shake-up. While the burger brand remains well-loved and has outsize influence for a chain of its size, the stock's performance has been mediocre since its 2015 initial public offering (IPO), and the business does seem to have room for improvement.

For example, Shake Shack is targeting restaurant-level operating margins of 19% to 20%, which significantly lag behind those of peers like Chipotle even though Shake Shack has higher average-unit volumes.

A proxy battle isn't a silver bullet for Shake Shack even if Engaged wins the three board seats, but it could push the company to be more aggressive.

Its recent decision to add drive-thru restaurants has paid off, and the company could likely benefit from adopting other features of the traditional fast-food playbook.