The centre-left Social Democrats, one of the four parties in government, are taking their fight against tax perks for wealthy foreigners to Brussels.
The party says it wants to help coordinate a Europe-wide campaign against what it calls "increasing competition" among countries seeking to attract the rich and famous.
Switzerland – which is not a member of the European Union - is famous for the special tax deals offered by certain cantons to attract wealthy foreign residents.
Music stars Tina Turner and Shania Twain are just a couple of the famous names who were apparently lured to the country as much for the generous tax breaks as for the alpine views.
It is estimated that around 3,000 wealthy foreigners are currently benefiting from fiscal incentives.
The number is expected to rise following the ratification of an accord between Bern and Brussels on the free movement of people.
The Social Democrats argue that Switzerland is one of many countries in Europe competing to lure billionaires.
Search for support
Senior party official Matthias Manz told swissinfo he would use a meeting of centre-left parties in Brussels on Thursday to build momentum for a concerted effort to stamp out the practice.
"The problem is... that exaggerated tax competition is a danger for healthy public finances," he said.
"We see this going on both within Switzerland between the cantons as well as between European countries, and we want to focus attention on this problem.
"Our aim is to discuss this issue, see whether other [centre-left] parties share our concerns and come up with a common position which could be implemented within the EU and Switzerland."
Supporters of a relaxed tax regime for rich non-Swiss citizens argue that the system allows local authorities struggling with public-spending cuts to gain additional revenue.
But Manz says this is not sufficient justification for maintaining the status quo.
"Sure these [rich non-Swiss] people are contributing to the public finances, but they are contributing much less than they should be when you consider their income and wealth," he said.
"If Switzerland offers special tax rules, other countries will do the same and you end up with a race to the bottom, with every canton and country competing against each other [to attract wealthy foreigners]."
It is not the first time that the Social Democrats have attempted to put the issue on the political agenda.
Earlier this year Susanne Leutenegger Oberholzer, a Social Democratic parliamentarian, tabled a proposal in the House of Representatives aimed at abolishing the fiscal perks.
She said there was no need for such a system because Switzerland already offers enough advantages for rich foreigners.
But her argument that the incentives are unfair and undermine the morale of ordinary taxpayers fell on deaf ears - Leutenegger Oberholzer's motion was thrown out of parliament.
Manz denies he is making the trip to Brussels because his party has lost the fight at home.
"At first sight it looks like that... but the truth is that we were already discussing the issue of tax competition [with other centre-left parties] in Europe."
The Social Democrat rejects suggestions made by Christoph Blocher, a cabinet minister and member of the rightwing Swiss People's Party, that tax benefits should be extended to include wealthy Swiss citizens as well as foreigners.
"[All I can say is that] I would like to see the People's Party propose a nationwide vote on whether rich people should not have to pay the tax they are paying now," he said.
swissinfo, Ramsey Zarifeh
More than 3,000 wealthy foreigners with residency status in Switzerland benefit from special tax treatment.
About half of Switzerland's 26 cantonal authorities offer a lump-sum tax to rich foreigners.
The tax is calculated on a minimum amount – the equivalent of five times the annual rent or the rental value of the house the person concerned lives in.
90% of the beneficiaries live on Lake Geneva and the Valais, Graubünden and Ticino regions.