The Murdochs may end up with more than one media empire under their belts. Lachlan Murdoch the eldest son of mogul Rupert Murdoch, is part of a joint offer to buy a group of trade magazines that includes Billboard and The Hollywood Reporter, in what will be his second deal in as many weeks. Illyria, Murdoch's investment company, is bidding with Pluribus Capital Management, a new organization that includes James Finkelstein, who publishes The Hill and Who's Who, Matthew Doull, former publisher of Wired, and George Green, former publisher of Hearst International. The bid for most of Nielsen Business Media could be announced as early as this week. Nielsen is reportedly seeking $70 million for its magazines and trade shows in a disposal that could precede an initial public offering.