The big problem is that the First Past The Post system always devolves into 2 parties. Let's say a Progressive Party launched tomorrow and got 25% of the left leaning votes. Some of those people would be folks who didn't vote before, but many would be Democrats who feel this party represents them better.
This isn't a bad thing in and of itself. People should be able to vote for parties that represent them the best. I'd be upset if my only ballot choices were "Classic Republican" or "MAGA" because neither would represent my views.
However, remember that many of the hypothetical Progressive party's voters would come from Democrat voter rolls. This would mean that Democrat support would drop. Again, not a bad thing but itself. Keep up with the times or get left behind.
The problem comes when the Democrats drop so low that Republicans start winning elections due to the Progressives pulling votes away. Maybe this is all temporary and would eventually right itself when the Progressive Party becomes the dominant party. Still, there would be a stretch of time when Republicans would rule nearly uncontested.
Just looking at Congress, imagine a Congress that was 70% Republican, 15% Democrat, and 15% Progressive. Items like a national abortion ban, banning any mention of LGBTQ, shooting illegal immigrants on sight, and arresting liberals for speaking up would have a shot at passing and wouldn't be able to be stopped. Even if the situation righted itself eventually and the Progressive Party took control by enough to enact their agenda, they'd have a massive mess to clean up.
That's why we need Ranked Choice Voting or Approval Voting first. It would let third parties grow without taking votes from the closely aligned major party.