I think the only way the two party system ends if one party gains enough of a majority to form a one party state (Like Singapore or California where opposition is legally allowed but has no real chance of power). Third parties aren’t viable in first past the post system.
Given favorable demographic trends and voters preference for left wing welfare state and social policies, the Democrats are far more likely to achieve this goal than Republicans. DC statehood, continued control of under 50 vote through popular culture and education system, increased immigration from more Dem sympathetic countries, and eliminating filibuster would be playbook (easier said than done).
"Dem Sympathetic countries" Well I'm sorry the Democrats don't advocate for the destruction of their countries and all immigrants.