There is significant research into overconstrained 6, 7, 8+ bar linkages. For reference, an overcostrained 4 bar linkage is quite common, your standard “4-bar linkage”. The fun continues as you add more and more linkages.

I’m no expert, but I understand that there is no closed method for determining viable overconstrained sets past 4. So the research has a large amount of analytical/exploratory research. Very active field: https://www.google.com/search?client=safari&hl=en-us&ei=1bvk...