A trio of candidates is on course for the best showing by third party or independent candidates in nearly two decades, but significant barriers remain to disrupting or dismantling the nation’s two-party system.

If opinion polls are correct, , and are likely as a group to receive a level of support unseen since consumer advocate Ralph Nader’s run for president on the Green Party ticket in 2000, when he drew roughly 3% of the national vote.

Mr....