How can a plane be cheaply owned by multiple people?
what you describe could be called a flying club or shared ownership. These sorts of arrangements are common enough that you should be able to find a template for setting up one which contains the details of how maintenance and overhead are covered and how the club's finances must be recorded and reported.
The cost effectiveness and fairness are determined by how money flows into the partnership and how it flows out. I would suggest you look into the Experimental Airplane Association's documentation on airplane ownership.