A small firm I know back home in Texas wanted to take over a similar, though much smaller firm in the EU. The EU firm had a turnover of about 2.5% (i.e. one fortieth) the size of the Texas firm. The EU said come on in, welcome, and we will tax you on all of your U.S. income, too. The deal finally went through, but not for 18 months spent making the EU firm a completely independent entity.
Knowing the EU, they will gladly work in language forcing a multinational to pay 15% in taxes on its worldwide income to each country in which it operates, which would make it liable for 105% of its income if it operates in 7 countries. Faced with that, the obvious thing to expect is for the multinationals to bribe enough officials to enact loopholes permitting them to pay even less than they pay now.
If done intelligently and fairly, the biggies probably wont bother to spend the money to fight it. If done stupidly, the only ones to get rich will be the lawyers and a few corrupt politicians.