BRUSSELS — The European Commission is considering watering down a tax on big businesses designed to raise money for the EU’s next seven-year budget, four EU officials with knowledge of the discussions said.

In an attempt to overcome resistance from national capitals, the EU executive is planning to reduce the number of companies covered by the new levy.

The Commission is considering exempting less profitable firms and raising the eligibility threshold to carve out small and medium-sized enterprises. But critics warn that cosmetic changes will not be enough to facilitate an agreement.