The political Party was the SA, the SS a small, but later much larger, subdivision of the SA- not separate Parties. Trotskyites were merely complainers who wanted Leninists to take a revolution to every nation in the world, not a separate political Party. They were later involved in Britain's Labour Party and pushed to have all major businesses and the property owned by anyone and nationalize it- communism, not socialism.
So, is the Republican Party a subdivision of the Democratic Party or is it the other way around? And there are multiple political parties besides the Ds and Rs. The Green Party, the Libertarian Party (I assume they still have a political Party), the Socialist Party, and many others have existed throughout the history of the U.S. None of them have gained enough traction to take on either of the 2 largest political parties. And, by the way you're using it, I'm not sure you understand what 'good-cop bad-cop' means.
It doesn't matter how many political Parties exist or whether an economy is capitalist or communist or 'hard-core' socialist, or even the one I could get behind if there was a true shot at gaining usable power, a 'Socialist Democracy', the end result- which would take longer to happen under some systems than others is one-Party rule- is totalitarianism. Until then I refuse to vote for any right-winger/Party-over-people candidate. And some of those people are Democrats but the vast majority are Republicans. At least the Democratic Party allows multiple viewpoints to be heard, at the risk, however, of losing power to the Republican Party because some 'factions' within the Democratic Party that claim to have the same end goals as other 'factions' but refuse to work with certain others that hold a different idea on how to reach said goals. Were Democrats the ones who began the 50-year long attack on Unions? No, the Democrats, starting with FDR, defended unionization and every American gained enormously due to labor Unions. Are the Democrats responsible for stirring up the hatred of the 'Other' and January 6, 2021? Or those people who are stupid enough to believe they can, with their much-loved military assault-style weapons, overthrow the U.S. military (can you imagine the damage a single Black Hawk attack helicopter could do to an entire neighborhood, let alone military special forces trained in urban 'guerrilla warfare, rather than running through the woods and playing a grownup version f Cowboys and Indians) but in the meantime just attack, verbally and physically, people not like themselves, not white and 'Christian'? No. Or of massive tax cuts for the few at the top of the wealth brackets and for big bossiness that makes huge profits but pay no taxes? No. Of the 'trickle down economic theory that is actually a trickle, no, a gush upwards to those who already have more that 80 to 90 percent of al wealth? No.
Are some Democrats as guilty as modern Republicans? Yes, of course they are. Would I support or vote for them? Only if the Republican candidate is worse. And in my 42 years of voting in every local, state, and national election, that has happened only once.
I'm not clear why you say that "true republics have multiple parties' when that's what this nation has had since soon after its founding.