Every connected manifold of dimension at least 2 is n-homogenous for every finite n. This in particular includes the example of the plane.

In my humble opinion, the cleanest way to define a local coefficient system is as functor from the fundamental groupoid to abelian groups. This works for all spaces without any assumptions and has good functoriality. The most comprehensive account of homology with local coefficients that Im aware of is in Whitehead's book "Elements of homotopy theory".