Shire logos sit on the boxes of Elvanse tablets and Mezavant XL tablets, produced by Shire Plc, on Tuesday, July 8, 2014.
(Simon Dawson/Getty)

Update, 7/18/14, 10 a.m. EST: This story has been updated to include the names of Sullivan & Cromwell’s deal team.

After being rebuffed three times by Shire PLC, AbbVie Inc. announced Tuesday that it was sweetening its bid to buy the Irish pharmaceutical company in a renewed attempt to reincorporate in the U.K.

The latest offer of 30.1 billion pounds ($51.5 billion) represents an 11 percent increase over AbbVie’s previous bid for Shire. It calls for AbbVie to pay 22.44 pounds ($38.44) per share in cash and issue 0.8568 of its own shares for each Shire share. In addition, Shire shareholders would own 24 percent of the company.

As part of the deal, AbbVie would move the combined businesses to the U.K., where it would set up as a holding company, according to The Wall Street Journal.

Advising AbbVie on Tuesday’s proposal are Herbert Smith Freehills and Sullivan & Cromwell; Shire turned to Slaughter & May and Davis Polk & Wardwell.

AbbVie, a North Chicago, Ill.-based pharmaceutical company, publicly acknowledged for the first time last month that it had made three separate offers for the Irish drug maker in May. But unlike those proposals, AbbVie and its financial advisers have now spoken with the majority of Shire’s shareholders on its latest bid. As with its other offers, the company is conditioning the deal on the unanimous backing of Shire’s board of directors. AbbVie added, however, it could waive that condition.

According to U.K. law, AbbVie has until July 18 to make a formal offer for Shire. Beyond securing Shire’s approval, the deal must also receive the blessing of regulators and AbbVie’s shareholders.

Shire said in a statement that its board would meet to consider the latest proposal.

AbbVie’s bid is the latest among a tide of so-called corporate inversions, in which U.S. companies seek to lower their tax obligations by relocating overseas. Pharmaceutical company Medtronic announced in June that it was purchasing Covidien for $42.9 billion in a bid to move to Ireland. That deal followed a failed attempt in May by Pfizer to purchase AstraZeneca for $119 billion—a move that would have allowed Pfizer to relocate to the U.K.

AbbVie, which was formerly the research branch of Abbott Laboratories before its $54.4 billion spinoff in 2013, heralded the new tax structure among the reasons in favor of the acquisition, referring to it as a “competitive tax domicile” in its June statement.

Shire itself chose to abandon its British residency in 2008 to enjoy Ireland’s lower tax rate and tax-free treatment of patent royalties.

Shire’s products are aimed at people suffering from serious health conditions, with facilities that focus on neurosciences and rare diseases. The company earned $4.9 billion in revenue last year, with more than 40 percent of its product sales coming from Attention Deficit Hyperactivity Disorder products.

While AbbVie also develops products to treat serious diseases, it maintains that the two companies would complement each other, adding that Shire would stand to benefit from the company’s research capacity, as well as its resources and scale.

For example, AbbVie noted that the acquisition would allow Shire to access the company’s broad international network. AbbVie has sold its products in more than 170 countries—a far greater number than the 50 countries where Shire markets its products.

However, these factors had not been enough to convince Shire’s board of directors, which had earlier criticized the first three offers for undervaluing the company and not adequately considering its growth potential. The board also outlined concerns about “execution risks associated with the proposed inversion structure.”

AbbVie sought legal counsel from Herbert Smith Freehills and Sullivan & Cromwell on its bid for Shire. The team from Herbert Smith Freehills included corporate partners Gillian Fairfield and James Palmer, M&A partner Stephen Wilkinson, and associate Adam Charles. Herbert Smith Freehills has handled patent litigation for AbbVie in Europe.

The Sullivan & Cromwell team included antitrust partner Steven Holley, executive compensation and benefits partner Matthew Friestedt, and M&A partner Matthew Hurd. Associates Scott Crofton, David Goldin, James Hu, and Regina Readling were also involved in the deal team.

Hurd, who co-leads the firm’s health care and life sciences practice, has worked on numerous pharmaceutical deals in recent years, and was named Dealmaker of the Week in 2011 for his role in HIV-medicine producer Gilead Sciences’ $11 billion acquisition of Pharmasset, a clinical-stage drug company.

For its part, Shire sought legal counsel from Slaughter & May and Davis Polk. The Slaughter & May team included corporate partners Adam Eastell and Martin Hattrell, and M&A partner Stephen Cooke. Associates Francesca Harris, Paul Mudie and Emma Plaxton also worked on the deal team.

Slaughter & May advised Shire in the company’s 2008 relocation to Ireland.

The team from Davis Polk included corporate partners William Chudd and John Meade, litigation partner Lawrence Portnoy and counsel Scott Luftglass, M&A partner and practice cohead George Bason, and tax partner Michael Mollerus. Associates Daniel Brass and Michael Patrone were also involved.

Davis Polk has advised Shire on a number of acquisitions in recent years, including a $260 million acquisition of Lumena Pharmaceuticals in May.

Both Slaughter & May and Davis Polk advised Shire on its $4.2 billion acquisition of rare-disease drugmaker ViroPharma Inc., announced last year.