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Ordinal voting systems cannot support third parties due to Arrow's Impossibility Theorem.
I don't get why RCV proponents constantly lie about it. But then again, it doesn't actually fix the problems present in First Past the Post, because at its core, Ranked Choice is First Past the Post, just repeated a bunch on a single ballot.
That leads to some odd situations where you can actually decrease support for your preferred candidate to help them win.
How that one works is if you have A, B, and C, with the election normally being a contest of B and C, C voters can strategically boost A until B is knocked out of the election. Then B votes get redistributed, with a percentage going to C, so that C now wins.
All because C lowered their first round support a bit, while demonizing A among B voters.
This same sort of mechanism has resulted in odd candidates winning real world elections. Like the Burlington, Vermont Mayoral Race of 2009.
Also, if you add more candidates to the ballot, this sort of attack becomes easier, not harder.
Then there's Ballot Exhaustion. This is where your ballot no longer has any viable candidate left to transfer votes to. But here's the kicker, your ballot can be gutted down the middle before your vote can transfer. If you have A, B, C, D, and E, on your ballot and B, C, D, and E, get eliminated before A, your vote gets thrown away. Even if transferring it to B, C, D, or E would have had them win. It doesn't matter at all, because the rules of the system so that those candidates are out.
Even if literally every single voter puts B as their second choice, with no other candidates reaching that magic 50% in the first round, B is eliminated.
And about that magic 50%. It's not 50% of the initial vote, it's 50% of the ballots that are left in that round. So with Ballot Exhaustion sometimes reaching as much as 18% of all ballots cast, you can have a winner who is only supported by 41% of the population. Or rather, 41% of the voters in that election.
Let's see, other red flags... RCV needs to be counted in a centralized location, so you have to transport the ballots. That adds to the time that counting takes, and adds security issues. Makes it very easy for the people counting to steal an election.
Then there's the complexity of the count itself. That has caused problems, like the wrong candidate being sworn in, because the people counting screwed up.
https://abc7news.com/ranked-choice-voting-oakland-school-board-director-district-4-race-mike-hutchinson-alameda-county-registrar-of-voters/12626221/
Overall, the system is actually a step backwards from what we have, and gets in the way of actual election reform, because people say "we already tried that, and it made things worse".
The actual reform needs to be a Cardinal voting system, Like Approval or STAR. Cardinal voting systems actually live up to the promise, and allow third parties to grow and flourish without punishing voters for wanting something different.