It is the fifth takeover offer from Takeda, which encompasses £27.26 in new shares and £21.75 in cash, implying a value of £49 per Shire share.
Takeda has upped its offer to buy Shire $SHPG for a mix of stock and cash worth close to $65 billion, which is good enough for the Lexington, MA-based biotech to extend the deadline on their talks to May 8 after determining they were close to finalizing a pact. The deadline could be further extended though if needed, said the Irish firm.
Takeda investors, however, reacted badly to the increased bid, which is up from the £42.9 billion ($60 billion) the company offered previously.
There is still work to do though - other terms of the revised proposal need to be agreed, Takeda must complete its due diligence review, and both boards must approve the deal.
A deal would significantly boost Takeda's position in gastrointestinal disorders, neuroscience, and rare diseases, including a blockbuster haemophilia franchise.
London-listed shares in Shire closed at GBP39.30 on Tuesday.
A takeover would be a continuation of Takeda's expansion plans under CEO Christophe Weber, the company's first ever non-Japanese leader, who has set himself the task of reinvigorating the firm.
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Takeda added in its own statement that it meant to maintain its dividend policy and investment-grade credit rating following the deal. "This huge acquisition bodes a spike in leverage that could result in a multi-notch downgrade", said analyst Yukiko Asanuma. On Wednesday, February 14 the rating was maintained by Piper Jaffray with "Hold". A Takeda-Shire transaction would be by far the biggest.
Dealmaking has surged in the drug industry this year as large players look to improve their pipelines.
Shire has always been seen as a likely takeover target.
This isn't the first M&A bid for Shire - a $52 billion takeover by AbbVie had been agreed but was terminated in 2014 because of a change in U.S. tax rules.
Allergan Plc, the USA maker of Botox, had been considering a rival bid for Shire but ruled itself out of making an offer last week.
Shire traces its roots back to 1986, when it began as a seller of calcium supplements to treat osteoporosis, operating from an office above a shop in Hampshire, southern England.
On Friday, Takeda offered to buy Shire for about $62 billion.