Not that easy to do, especially since the 2 Parties have arrogated the unConstitutional power to grant favors and preferences to their chosen groups in exchange for votes and money. Their ability to enact unConstitutional statutes is little different from the King permitting the peasants to bring their requests to their Master in exchange for property or service to the King. A good example of this lies in the way our illegal Tax Code functions. The Parties can submit legislation that gives a tax benefit or exemption to one American citizen (or group) at the expense of another American Citizen. Yet the Constitution mandates that all taxes be "uniform" and none can be based on one's productivity (income).
This is only one example, however. Because the government is allowed to operate unConstutitionally, it can operate as a King -- doling out favors, privileges, benefits, etc. Thus, to participate in the system, individuals and groups must organize and offer money, votes, and quid pro quo arrangements to their Party in order to be the beneficiary of the government's omnipotence.
Any new or principled Party, who might be reluctant to participate in this illegal and corrupt process would have little chance of making inroads into the existent power structure. There is no doubt, a power monopoly can oppress and even eliminate its competition. After all, that's what monopolies do.