Editor's Note:  A previous version of this article incorrectly indicated that Vyvanse was currently approved for binge-eating. It will reportedly be submitted for approval during the third quarter of this year. The Fool regrets the error.

The market is already looking for AbbVie Inc (NYSE:ABBV) to sweeten its recently rejected cash-and-shares offer of $46.5 billion for British drug maker Shire (NASDAQ:SHPG).

But, by how much? And, assuming AbbVie comes up with yet another offer, will it be enough to fend off Shire's other potential suitors?

While perennial M&A target Shire officially torpedoed AbbVie's third and latest bid last Friday, Jefferies analysts are now suggesting the deal could go through if it was raised to $55 billion, according to Reuters. Why so high? Taking a page from AstraZeneca's playbook when it broadcast its long-term sales ambitions, the firm's boss made a pledge to shareholders to turn Shire into a world-leading biotech firm.

To be specific, on a Monday afternoon conference call, Shire's CEO Flemming Ornskov outlined a plan to bootstrap the company's late-stage development pipeline from $5 billion to $10 billion in annual sales. The CEO's projections were well ahead of even favorable analyst forecasts for Shire, which run around $8 billion by 2020.

Ornskov cited sales of at least $1 billion for lifitegrast for dry eye disease, but data from late-stage clinical trials in April were so-so, with lifitegrast meeting a primary endpoint for patient-reported improvement of dry eye but missing the other primary endpoint for corneal staining.

Ornskov, who took the helm at Shire only thirteen months ago, can't be faulted for his ambitions for Shire, having already conducted six deals during his short tenure. There are other opportunities too -- Vyvanse, currently approved for ADHD, will reportedly be filed for a label expansion into binge eating later this year (of course, whether the FDA will approve the drug for that indication is unknown). Ornskov also said his projections did not include any further deals or take into account drug potential from recent acquisitions.

Other suitors waiting in the wings?
Analysts at Charles Stanley believe AbbVie may well step back in with an even more substantial offer. AbbVie badly needs to reduce its almost total dependence on rheumatoid arthritis drug Humira. The drug gave AbbVie a big boost last quarter, but Humira accounts for a huge percentage of AbbVie's top line, and it is only two years away from losing patent protection in the U.S. While AbbVie probably has a winner in its interferon-free cocktail for hep-C treatment, it is facing a huge revenue loss with Humira that must be filled.

Perhaps even more significant, nabbing a company on foreign soil would allow American multinational AbbVie to become the latest pharmaceutical company to relocate overseas. Such so-called "inversions" by U.S. companies are front-and-center in the pharmaceuticals sector this year, with firms paying high tax rates vying with each other to make deals that will keep them competitive with rivals already enjoying lower taxes.

Nevertheless, reducing tax bills is rarely the only motivation for such megadeals. Inversions allow companies to access cash more easily and make future acquisitions more attractive by sheltering foreign earnings overseas.

Shire's tax advantage--not to mention its pipeline of fast-growing specialty and rare-disease drugs--has attracted interest from companies like Bristol-Myers Squibb, Merck and Pfizer. But the one company (besides AbbVie) most likely to make an imminent move on Shire is Allergan (UNKNOWN:AGN.DL). Shire rebuffed Allergan once before, and the deal doesn't make nearly as much sense from a business perspective, but timing is everything in the M&A world. Allergan is in a mad scramble right now to avoid Valeant's hostile takeover. There are also some potential areas of overlap between the two companies in eye disease.

Shire may even decide to do some more M&A on its own. "Going on a bit of a shopping spree makes it harder for another entity to go after them," Piper Jaffrey analyst David Amsellem told Bloomberg earlier this month.

"Discussions are no longer on-going," AbbVie said in a statement. Nonetheless, people briefed on AbbVie's plans say it has not abandoned its interest in Shire.

With Shire trading around $224 as of this writing, above the pre-offer price of around $192 on Thursday, it's pretty clear the market still hopes a deal may be signed. But a wrench could be thrown in the works from an unexpected source. The inversion frenzy has sparked attention that could reverberate through the sector. Recently, Sen. Ron Wyden warned in a Wall Street Joural op-ed about Congressional plans to crack down on corporations that shift their tax addresses overseas through inversion deals.

It could get very interesting--and not just for AbbVie and Shire. Stay tuned.