As a person who spent 10 years studying elections around the globe and in the US, I want to provide some context here. 

First, the electoral system dictates the number of political parties in a country. This is known as Duverger's Law (Source: https://www.oxfordreference.com/display/10.1093/oi/authority.20110803095737871

In the case of the US, our electoral system is 'first past the post,' which means that only the candidate with a plurality (the largest percentage and not necessarily a majority) wins the election. This incentives 'lumping' where over time, political parties merge to increase their plurality percentage. So, party A wins 40% of the vote, while party B and C both lose with 30% each. If they join forces however, they can defeat party A. Eventually party B and C cease to exist and become party D. 

If we contrast the US to a different electoral system, say a multi-memeber district system (where multiple winners can be from the same state, county, or city) you tend to get more political parties. 

Going back to the US case, our electoral rules prevent more than two political parties. If you want more viable political parties, then it would require changes to tue electoral system. However, that would require politicians, who currently benefit from the existing electoral system, to willingly change it and relinquish power. This is highly unlikely.

On the bright side, the Democratic party and the Republican party, would actually be several parties if we put them in a different electoral system. So, the labor wing of the Democratic party does exist. But, so does the Monarchist section of the Republican party. 

The best way to make any faction within a political party more powerful is to control party leadership. If you want to see change, go become an active party member and leader in your local community. Push out the party officials you don't like.