Yes. Each county/parish runs their own election in the US. Sometimes municipalities have their own elections, but many times it’s part of the county or parrish elections.
Our city actually had their own election during odd years, but turnout was so poor for standalone city elections that they decided to integrate these elections alongside the county (state and federal) elections.
Would it be difficult to have four separate ballots? I think it could be implemented, but it might take more people power to scan the ballots and follow up with a hand count if necessary. Our election workers get paid, but unlike jury duty it’s not compulsory. Employers would balk at giving their employees time off to work an election.