Late Tuesday Shire reported that Takeda had upped its bid to £27.26 in new Takeda shares and £21.75 in cash, coming to £49 a share.
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.
The Friday offer valued Shire at £47 ($65.50) a share, up from £46.50 ($64.86).
But Takeda's shares extended recent losses, tumbling 7 percent as investors fretted over its ability to buy a company twice its size, raising doubts about whether Shire shareholders will accept a bid that is 56 percent in new Takeda shares.
The offer values Shire at approximately £46bn and shareholders will be entitled to any dividend prior to the takeover, which will see shareholders own 50% of the enlarged Takeda.
The Irish drug giant, which has a strong portfolio of rare disease treatments, has recommended to its shareholders a revised bid from Takeda.
Jefferies analyst David Steinberg said: "While this offer represents a solid improvement over Takeda's third bid (38% cash), we still wonder if it is enough to satisfy Shire shareholders".
The company also expects to get a balanced geographic footprint, enhanced financial strength and a modality-diverse pipeline through the merger with Shire.
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.
Takeda, now worth $33 billion by market value, had 466.5 billion yen ($4.3 billion) in cash and short-term investments as of end-December.
Shire has always been seen as a likely takeover target and was almost bought by USA drugmaker AbbVie Inc ABBV.N in 2014, until US tax rule changes caused the deal to fall apart.
Shire also announced last week it was selling its oncology business to unlisted French drugmaker Servier for $2.4 billion.
Takeda bought U.S. biotech Ariad Pharma for $4.7billion previous year, although many market commentators felt this was overpriced.