LONDON (The Deal) -- Luxembourg takes over the EU's rotating presidency this week amid a storm of controversy over its dubious distinction as a tax haven for multinationals from Walt Disney (DIS) - Get Report to Coca-Cola (KO) - Get Report.

The companies are among more than 340 firms who allegedly shifted profits to the Grand Duchy through sweetheart tax deals uncovered in last year's "LuxLeaks" investigation. Some even slashed their tax bills to below 1% of profit.

It's been bad public relations for European Commission President Jean-Claude Juncker, who was Luxembourg's prime minister when many of the deals were made and survived a censure vote in the European Parliament early on in his term.

The Juncker Commission is now cracking down on corporate tax dodging along several fronts.

In the antitrust field, E.U. competition chief Margrethe Vestager is leading in-depth probes into Luxembourg transfer-pricing arrangements forAmazon (AMZN) - Get Report and Fiat Finance and Trade, part of Fiat Chrysler Automobiles (FCAU) - Get Report, and into similar set-ups forApple (AAPL) - Get Report in Ireland and Starbucks (SBUX) - Get Report in the Netherlands.

Competition officials are also pressing 15 EU governments to provide information about tax rulings from 2010 to 2013 to see whether they grant companies selective tax advantages in violation of E.U. state aid rules. They've even threatened Estonia and Poland with court action if they continue to ignore information requests.

"We are putting together the puzzle of tax ruling practices in the E.U.," Vestager said in June. "Sometimes we have to ask member states twice -- or more -- to provide information."

Unwilling to leave the commission to its own devices, E.U. legislators have set up a Special Committee on Tax Rulings, chaired by French center-right politician Alain Lamassoure, to conduct a separate investigation. The committee has been publicly grilling experts and representatives of multinational corporations, with the next meeting scheduled for July 2.

As the E.U.'s executive branch, the European Commission is the only institution that can launch proposals for new legislation.

It wants to see companies taxed where profits are made and re-launch a 2011 proposal for a common consolidated corporate tax base that would allow companies doing business here to calculate their E.U.-wide taxable profits instead of having to deal with 28 national systems. Both were outlined in an action plan adopted earlier this month, part of a longer-term goal to jump-start jobs and growth.

"Every day in Europe, there are companies making profits and not paying their fair share of tax," said EU Tax Commissioner Pierre Moscovici. "The Commission has promised to fight against corporate tax avoidance, and today we are making good on that promise."

As with any tax proposals, any reform will need unanimous approval from all 28 EU countries to get off the ground. That includes Luxembourg, which will chair all technical and political-level gatherings for the next six months in the EU presidency chair. While the government has pledged to make the fight against fraud and tax evasion a priority, it won't be easy.