Having multiple parties would require us to get rid of first past the post and/or geographically linked House seats. The former is possible as the States can determine their voting process and some (mostly Maine if I remember right) have switched to Ranked-choice voting but not enough to matter. And that requires going state by state. The latter would require a constitutional amendment ... which won't happen anytime soon. The Brits have a similar system and a 3rd party, but barely and beyond the similarities the structural differences* make that impossible for us without major changes to our voting systems/government structure. Basically we've ossified and it's unclear how to change the system as the system makes it hard to change.
But there's no doubt that the current system is ... not great for anyone. Unfortunately though the far right is gaining ground everywhere, regardless of voting system. Our issues exacerbates the problem, but it isn't the underlying cause.
*The Brits are mostly single cameral with the Lords being sort of there as a delaying body and primary governance in the hand of the prime minister rather than a president. This allows for a weak 3rd party, currently the Liberals, to technically exist but only rarely matter. The Brits also thought about changing their voting system under pressure from the Liberals, but rejected it (this was the grand bargain the Liberals made with the Tories to give the Tories power which eventually led to Brexit, all to try to get rid of First Past the Post which failed - the one time the Liberals mattered).