They would become factions within the GOP and they would have more influence than they do now.
I can see you've given this some thought. The problem is (at least in my experience) many 3rd party types seem to be more interested in being ideologically pure than winning, many of them have left the GOP because they couldn't compromise on (incert your issue here).
"I support the rightward most VIABLE candidate."
WF Buckley
I've run into many here who just can't accept that idea.
Well time for this buck-a-roo to head for the old bunkhouse.
That reminds me of his running for NYC Mayor... "Unmaking of a Mayor" I think was the title of the book.