Radical Euroskeptic parties, including France’s Front national and the United Kingdom Independence Party, picked up dozens of extra seats in the European Parliament this weekend. Yet their influence could be limited, given the hostility of mainstream parties toward them. Rather, the mildly Euroskeptic group that is led by Britain’s Conservatives and Poland’s Law and Justice party could matter far more.

British prime minister David Cameron’s party lost seven seats and the European Conservatives and Reformists, a group he helped establish in 2009, lost eleven overall. Compared to the two other right-wing blocs in the European Parliament, which lost more than eighty seats combined, that wasn’t such a bad performance — especially when parties from other countries are likely to join.

Europe of Freedom and Democracy, a group that is led by the United Kingdom Independence Party, is competing with Marine Le Pen’s more hardline Front national and Geert Wilders’ Freedom Party in the Netherlands who intend to form their own bloc. Italy’s Lega Nord is expected to leave the group and join the latter. The Danish People’s Party, by contrast, is courted by the European Conservatives and Reformists. It won four seats, more than either the ruling Social Democrats or the liberals.

The Sweden Democrats, a similar party, is likely to join Le Pen and Wilders but the Finns Party (formerly the True Finns) has refused to enter an alliance with them. So have the Flemish nationalists who won Belgium’s federal election on Sunday. Both are more closely aligned with the Conservatives.

There are also Euroskeptics in Bulgaria, Croatia, Germany and Slovakia looking for a political group to join. They could help the Conservatives and Reformists cross the threshold of 65 seats which entitles any group to extra positions, such as a second committee chair.

The group enjoys more influence in any event than fringe Euroskeptics. Whereas the established parties largely shun those who want their countries to leave the European Union altogether, the reformists are part of the legislative process even if they don’t share the desire for ever-closer union that seems to come instinctively to most other members of the European Parliament. They could therefore have a moderating influence in an assembly that tends to find pan-European solutions for every problem — perceived or real — in Europe.

However, the addition of more parties from other countries would also dilute the British Conservatives’ influence within the bloc. Whereas they used to have more than three times the number of seats as the Czechs and the Poles, giving them by far the most clout, their losses this weekend, combined with a strong showing for Poland’s Law and Justice party, could lead to changes in the party platform. The Poles in particular are supportive of the free movement of labor in Europe, which the British want to curtail, and altogether more positive about European Union projects and spending.