The next new party that will challenge the two party system will evolve from the internet. I don't know what its politics will look like but it will probably be ugly and snowflake driven.
You will have the sjw/snowflake party and the patriot party that will not have social issues as it's core tenant.
Patriot party will be small gov't, low taxes, low regulations, won't care about gay marriage, pro 2nd amend, prob a mix of pro choice and pro life (Tomi Lauhren types-lot of them gals out there), strong borders, strong nationalism.
The people I see on FB, the majority of them who talk politics fit to the t above-combination of libertarian and conservatives. Most Trump supporters fit this category