Realistically, the party would split, as it's already a clusterf*ck of (sometimes incompatibile) ideologies. From the schism you'll get back to a 2-party situation, the biggest two subsets. Ex-republicans that haven't retired from politics would join the more conservative of these two.
You'll get two shiny two parties but unless the voting system is reformed, it'll be essentially a façade change. "Progressives" vs "Conservatives" (or whatever names they'll pick), green vs pink, instead of "Democrats" vs "Republicans", blue vs red.