Well, two things. First, the tea party did exactly that and it didn’t fix first past the post. They just tanked the Republicans, and then melded it into the Republican party the next season.

Second, there are a certain number of Americans that will vote Republican or Democrat because that is what they self-identify as. That number is about 30% of the voting population. So for a third party to be viable, they would have to take all of the independents, and then break some people of their identity.

So is it possible? Yes. Will you ever be able to do it? No. It’s possible the same way winning the lottery is possible. I.e. it feels like a chance to people who are bad at math.