It’s certainly possible and likely. The way I interpreted the question asked wasn’t about how to get the Socialist Party to win a presidential election, but to make it become a mainstay with enough infrastructure as an institution to remain competitive on local and state levels for a significant period of time. The Socialist Party was already fielding a wide range of candidates in 1912 and was beginning to build city-based political machines like with the election of Berger in Wisconsin. In Oklahoma, it was becoming a significant force in state politics as well. World War One introduced pressures that would severely depress its membership and eventually break it into competing factions, but absent those pressures I see this process continuing. Even if it isn’t a party that is getting 50% of the vote nationally, I think it’s plausible to have it replicate the successes of Minnesota’s Farmer-Labor Party and become a fixture of multiple states in the country. Eventually they would probably get subsumed by one of the two major parties like how Farmer-Labor did during the New Deal, but I don’t think that end result contradicts the requirement of having it become a major party. And besides, the Whigs are an example of a major party failing to address serious contradictions in their voting base and being swamped by an up-and-coming third party. Even if the Socialist Party remains only regionally relevant into the 1920s, the stresses of the Depression and lack of a coherent response from either party could cause groundswell support for the Socialist Party that displaces the Democrats in key regions. Even if it isn’t likely, it’s possible. Impossible was the term I was objecting to.