Yes but if each house district is FPP 3rd parties generally don't get a look in, people who vote for them get no representation at all, and can produce governments where the party with the most seats got fewer votes than the others.

MMP provides local representation, and proportional representation (at the expense of having larger local seats, or more representatives).

Voters pick a candidate knowing that the candidate will have to play within a two party legislature.

Third party legislators are shunned. Their bills get no traction, and they get no committee assignments. If they are seriously divergent, the House could easily have them removed.

Further evidence for this exists in the demise of ticket splitting: if you vote R at the top of the ticket, you're very likely to vote R the rest of the way down the ticket, regardless of who the downballot R's are. It wasn't always this way, but has been for some time.

Some States even have a single box you can check to vote entirely for that party’s candidates, “straight ticket voting”.

Texas removed it a few years back and it’s removal was challenged (and lost) by Democrats: https://www.texastribune.org/2020/09/30/texas-2020-election-...