Lots of Netflix investors seem to believe that the corporate raider has enough ideas and juice to revive the video rental company, which is struggling to secure its place in the media ecosystem. Shares only retreated 3% since Wednesday, when they popped 13.8% on the startling news that Icahn bought stock and call options that could give him 9.98% of the company. That resulted in widespread speculation that the legendary crusader for shareholder value has a plan to force Netflix to take a new direction following nearly a year and a half period during which Netflix lost 74% of its market value.

Well, if he does, then it will be interesting to see what it is — and how he might prevail if he crosses swords with CEO Reed Hastings. Icahn has fewer options than people think.

Potent anti-takeover provisions in Netflix’s by-laws would make it difficult to wage a hostile effort to take over the board. The company’s staggered elections mean that only a third of the directors are replaced each year. What’s more, Netflix doesn’t allow shareholders to call a special election to pick new directors. If Icahn continues to buy stock, the company can exercise what’s known as a poison pill — a provision that gives the board the right to flood the market with up to 10M preferred shares, diluting the value of his holdings. Corporate law in Delaware, where Netflix is incorporated, also bars companies from combining with a holder of more than 15% of its stock unless the holder has had the shares for at least three years — unless the board approves the transaction.

Of course the board has a fiduciary responsibility to serve shareholders. Directors would have to pay attention if Icahn finds a buyer who’d pay a healthy premium over Netflix’s $4.3B market value. Other shareholders are so frustrated by the company’s rollercoaster ride that they “would be willing to partner with Icahn in his efforts to force a sale,” Barclays Capital’s Anthony DiClemente says.

The problem is that analysts see few likely buyers. That’s even true of the most frequently mentioned names: Amazon, Apple, Google, and Microsoft. Although they can afford a deal, none has a burning need to own a subscription video streaming service. Apple basically sells gadgets, Google’s committed to ad-based services, and Microsoft lives off its software.  That leaves Amazon as the only candidate “that makes strategic sense,” Wedbush Securities’ Michael Pachter says — although he notes that Hulu and Verizon (which is preparing to launch a streaming service with Redbox) are “engaged in a business sufficiently similar to Netflix’s that they could potentially justify an acquisition.” But Pachter says Amazon probably wouldn’t bite. It appears to have “made a conscious decision to build its service rather than buy,” he says. And if it wanted to buy Netflix, the odds of a deal are “less likely” now that Icahn’s jumped in and raised Netflix’s market value.

How about Big Media companies? They “enjoy taking Netflix’s money, without having to endure its low margins and lack of free cash flow,” BTIG analyst Rich Greenfield says in a note today. Each also seems to have special concerns. Anti-trust officials would stop Comcast from adding Netflix to its cable and broadband systems and NBCUniversal. Time Warner execs are determined to keep the cable programming bundle intact, although the analyst says that they could create a powerful next-generation television network by putting Netflix together with HBO and then spinning them off. News Corp prefers to build businesses rather than buy them, and has its hands full splitting off the publishing operations. CBS has promised to return cash to shareholders. Disney’s tied up with its $4B deal to buy Lucasfilms. Dish Network stubbed its toe on Blockbuster, and has little interest in overseas expansion. Greenfield says that AT&T might be interested, but only if it’s “worried by Verizon’s joint venture with Redbox” and wants to one-up them.

If Icahn can’t take over Netflix, and can’t persuade someone to buy it, then he still could shake things up by trying to pressure Hastings into changing policies that keep the stock price from appreciating. The most obvious target would be the company’s costly efforts to expand overseas. But Hastings has dug in his heels. Netflix “needs international to sustain growth, as the US shows early signs of maturity,” says Janney Capital Markets’ Tony Wible. Hastings “has shown he is willing to lose money for long term growth, while Icahn more typically targets near term cash flow opportunities that could detract from Mr. Hastings’ vision.” If the CEO wanted to score some debating points he need only note what happened the last time Icahn favored short-term fixes for a struggling home video business. As a board member of Blockbuster, “Icahn was against…technology investments that would have helped it to compete against [Netflix],” Wible says.