Mercer Island billionaire Paul Allen today renewed his effort to sue Apple, Google, Facebook, eBay, AOL and other companies for patent infringement.

Allen's case was rejected on Dec. 10 by a federal judge in Seattle who said it was too vague. U.S. District Court Judge Marsha Pechman told Allen he had until Dec. 28 to file an amended suit.

Just meeting the deadline, Allen filed an expanded version of the original suit with more details of how the companies allegedly infringed. The filing also includes 40 exhibits, many of which are screenshots of Web sites with modules highlighted.

Here's the filing: 2010-12-28 Interval First Amended Complaint for Patent Infringement (2).pdf

The companies being sued declined to comment on the allegations when the suit was first filed in late August.

Experts have said Allen's case is a longshot but the potential payoff is large - perhaps $500 million or more if he wins.

Defendants named in the suit are Apple, Google, Facebook, eBay, AOL, Netflix, Yahoo, Google's YouTube, OfficeMax, Office Depot and Staples.

Patents at issue in the case were generated by Interval Research, a Palo Alto, Calif.-based research venture that Allen, co-founder of Microsoft, and Xerox veteran David Liddle started in 1992. Allen closed it down in 2000.

Allen's suit alleges that his patents cover, among other things, systems that automatically call up and display related content. The approach is widely used by online retailers and other sites across the Web.

For instance, when viewing a product on Apple's iTunes store, the store automatically suggests related content that may be of interest. The suit filed today argues that this infringes on at least 20 claims made by a patent Allen holds.

Here's the exhibit submitted to illustrate the Apple violations: