Minnesota had non-partisan legislative elections until the early 1970s.
New Hampshire has an interesting electoral system in its state house. I forget the name of the system... but you have multi-member districts.
3rd party candidates have had some success in New England and Minnesota and 3rd party movements have always been relatively popular here.
NJ has multi-member districts, as well; each legislative district elects one Senator and two Representatives.
We have a similar setup... except each senate district is divided into A and B... each half electing one house member.
As for the Democratic parties being different in Minnesota... it's the same in North Dakota as well where the Democrats merged with the Non-Partisan League to become the Dem-NPL party.
The Democratic party in this region was basically a bastard 3rd party from 1860-1944 and the Farmer-Laborites were the 2nd party representing mostly radical socialist policies. In the 1910s and 20s on federal elections you had a choice generally between a somewhat progressive Republican and a radical Farmer-Laborite with the Democrats competing mainly in St. Paul among the Irish there.
Hubert Humphrey's flavor of social progressiveness on civil rights forced the FL party and the Dems together. Humphrey's 1948 convention speech was likely one of the first occasions where southern Democrats began to rebel.
I'm glad my state had a big part in ridding the Democratic party of conservative/reactionary southern whites. We loved Jimmy Carter but
not Strom Thurmond.