They had "multiparty" much like Canada does currently by the time the Nazis were a majority party.
As in, it was 2 major parties and satellite parties that barely made a difference. They just needed a bit of extra support to get the super majority, and to achieve this they got people to vote for the minority party which supported them, and ran propaganda to get people to vote for a minority party that was unpopular instead of their main opposition to divide the opposition vote.
So to reiterate the point, "third party" doesn't mean literally "a third party", much like in the USA it doesn't either; there's technically also other parties than just Democrats or Republicans, like the Green party and the Libertarian party. And much like the Nazis did, the Republicans supported and welcomed in the Libertarians while launching propaganda to divide votes from the Democrats to the Green party (the Green party itself likely compromised) in past elections.