supermajority 
noun (plural supermajorities)
A number that is much more than half of a total, especially in a vote.And requiring a two-thirds supermajority vote of the state legislature to pass a budget in effect paralyzes government....
- Many cities, for instance, allow a supermajority of homeowners to petition to make their neighborhood a historic district subject to special aesthetic controls - potentially a good model of specialized design boundaries.
- Before this can happen, he should be required to obtain a Congressional supermajority, and the requisite percentage should increase with every requested extension - from two-thirds to three-quarters to four-fifths.