Mylan N.V. again increased its offer to acquire Perrigo Co., now to $35.6 billion, the latest move in a three-way takeover tussle in the pharmaceutical industry.

Mylan's latest bid consists of $75 in cash and 2.3 Mylan shares for each share of Perrigo. Based on Tuesday's close, the offer values Perrigo at about $242.23 a share.

Shares of Mylan rose 0.2% in morning trading, while shares of Perrigo added 1.6%. Representatives for the two companies weren't immediately available for comment.

The previous offer, from April 24, consisted of $60 in cash and 2.2 Mylan shares for each share of Perrigo, and it valued Perrigo at about $222 a share, or about $33 billion. The April 24 offer was up from Mylan's earlier approach of $205, which was an unspecified mix of cash and stock.

Perrigo has rejected the previous bids, calling them too low.

On Wednesday, Mylan Executive Chairman Robert Coury said the company has made a "'hell or high water" commitment" to close the deal and obtain clearance.

Mylan shareholders would now own about 61% of the combined company, while former Perrigo shareholders would own about 39%.

Meanwhile, Mylan itself has been the target of a proposed $40 billion takeover from Teva Pharmaceutical Industries Ltd. Mr. Coury on Monday issued a stinging rebuke of Teva, questioning the credibility of Erez Vigodman, Teva's chief executive; repeatedly chiding Teva for a "dysfunctional culture;" and disparaging what he called a "poorly performing, troubled company" that has displayed "consistent underperformance."

Mylan and Perrigo generally compete in different segments of the generic-drug business. Mylan is best-known for selling generic prescription drugs, though its top-selling product is the EpiPen emergency treatment for allergic reactions. Perrigo makes over-the-counter cough-and-cold remedies and infant formula for chains like Wal-Mart Stores Inc. and Walgreens, which sell the products under their own names.

Neither company is a household name, but a combination of Mylan and Perrigo would create one of the world's top sellers of low-price medicines with $15.3 billion in yearly sales.

Under takeover rules in Ireland, where Perrigo is based, Mylan is obligated to make a public announcement once it has started the formal process of acquiring another company.

Write to Angela Chen at angela.chen@dowjones.com

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