Mithras, which owns 1.9 million Yahoo shares, calls its proposal a compromise deal. It would require that Yahoo rescind its so-called poison pill. That is an employee severance plan that Yahoo adopted after Microsoft's hostile takeover bid that some say would encourage employees to quit in the event of an acquisition and would allow some to collect generous severance pay. Because the plan could result in significant costs to a Yahoo buyer, some analysts say that it discourages a takeover.

The Mithras proposal would come with some risk and challenges for Microsoft. It requires Microsoft to essentially buy the whole company and then sell off the Asian assets and the non-search business, assuming that Microsoft would find buyers willing to take those businesses at current market value.

Beyond finding such buyers, Microsoft would also be faced with the challenge of technically separating the businesses, a potentially daunting task, Frank said. "I've been rather skeptical of what it would take to carve out Yahoo's search business from the rest," he said. "That's a challenging proposition." He said Yahoo has structured the organization in a way that integrates inventory management with search and display, for example, which would make it difficult to separate out the businesses.

This isn't the first time that Mithras has issued a proposal outlining terms of a potential deal between Yahoo and Microsoft. In July it described a deal where Microsoft would buy all of Yahoo for $33 a share.

As Yahoo's stock continues to dive, shareholders like Mithras are likely growing increasingly anxious. "Clearly a lot of these guys have lost money," said Parakh.