New Hampshire Representative Max Abramson has introduced HB 1214. It says that a group that is not a qualified party, but which has at least 500 registered members, may appear automatically on the November ballot. Such a group would nominate by convention, not primary.
The current definition of party is one that polled at least 4% at the last election for either U.S. Senator or Governor. The only qualified parties currently are the Republican and Democratic Parties.