Activist money manager Carl Icahn boosted his stake in nutritional-supplement maker Herbalife Ltd. (HLF), another move in a busy day for the billionaire investor that saw his involvement in several high-profile corporate sagas.

In a filing late Thursday with the U.S. Securities and Exchange Commission, Mr. Icahn disclosed that he increased his Herbalife stake to 15.55%, up from about 13%.

Herbalife shares, down 38% over the past 12 months, rose 1.6% to $41.65 in recent after-hours trading.

In addition to the increased Herbalife stake, The Wall Street Journal reported Thursday that Mr. Icahn had been in talks with Dell Inc. (DELL) over a potential bid for the company before Mr. Icahn pushed for a huge special dividend, citing people familiar with the matter.

Meanwhile, the tussle continued between Mr. Icahn and offshore driller Transocean Ltd. (RIG) over the company's dividend and board members, while separately Mr. Icahn voiced his support for commercial-truck maker Navistar International Corp.'s (NAV) new chief executive, Troy A. Clarke.

The Herbalife increase comes roughly a week after Herbalife agreed to name two of Mr. Icahn's designees to its board, as the company won new support in its ongoing battle with another hedge fund manager, William Ackman.

Under the terms of the deal, Icahn Enterprises LP and related parties agreed to vote their shares in support of all of the board's nominees. They also have the right to increase their stake in Herbalife up to 25%.

Herbalife has been embroiled in a battle with Mr. Ackman, who holds a large short position, a bet on a share-price decline, and has raised concerns about the legitimacy of Herbalife's business model.

Herbalife has called Mr. Ackman's allegations malicious and accused him of trying to manipulate its stock, a charge he has denied.

The company in February reported a 12% increase in fourth-quarter earnings and raised its profit outlook for this year.

Write to Anna Prior at anna.prior@dowjones.com

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