I said “replace,” not “compete in tandem with.”
If it were that easy, we'd have already done it. We hear this talk nearly every election cycle and it isn't going to happen. In this environment you'd have to compete with the existing Republican party for at least an election cycle or two - perhaps longer. The GOP isn't going to just say, "well gee, Yashcheritsiy and friends are going to fire up their own party now, lets just go away". Actual conservatives can dominate the Republican party and win its nomination, but it requires very good, charismatic candidate(s). Movement conservatives/Tea Party did not put one up this time around. Heck, we all can't even come close to agreeing on which of the last 2 candidates would be the best non-Romney, how do you expect to replace the Republican party when those kind of divisions exist?