There once was a party called Whigs,
http://www.history.com/this-day-in-history/republican-party-founded
I wondered how the Republican Party formed. Above is a concise story. I have not heard of any meetings held to discuss the formation of a new party as was the case when the Whig party dissolved. I would think that our Senators and Representatives and governors could quietly meet to gauge the interest. Then, a few of the more courageous among them could form a new party and set up the apparatus.
You wont find any leaders on their own willing to do this and nobody would follow one who did. No politician wants to be seen as the subservient follower of another. Theyre like tomcats in that regard. However, all the tomcats will show up to howl over a female in heat. Now, if we can just get the Democrats to threaten succession if the new party comes to power
And a splinter from the Republican party called the Bull Moose.