BRUSSELS — For decades, any European Union nation could block proposed laws in the most sensitive policy areas, like taxation, consigning them to the scrap heap if they encroached too much on its power.

But, as the union expands, the notion of universal consent is seen as increasingly unworkable and could be starting to break down. Legislators here are devising new approaches that will enable smaller groups of countries to adopt laws among themselves — without the threat of a veto if all 27 member nations fail to agree.

The move toward smaller groupings reflects a growing fragmentation of the European Union and has been developing for some time. But it took on added significance after a spectacular dispute at the European summit meeting in December, when Prime Minister David Cameron failed to achieve new safeguards from European Union laws for Britain’s financial-services sector. In retaliation, he blocked a proposed treaty change aimed at helping to strengthen the euro.

Under current rules, groups of at least nine nations may go ahead with legislation if an agreement has stalled. However, they can do so only after all 27 countries have been through the time-consuming process of trying and failing to agree. So far, that has happened in only two cases, but others in which this principle may apply are working their way slowly through the system.