Is it physically sound to add a topologically massive term to three-dimensional massive electromagnetic or gravitational models?

The addition of a topologically massive term to an admittedly nonunitary three-dimensional massive model, be it an electromagnetic system or a gravitational one, does not cure its nonunitarity. What about the enlargement of avowedly unitary massive models by way of a topologically massive term? the electromagnetic models remain unitary after the topological augmentation but, surprisingly enough, the gravitational ones have their unitarity spoiled. Here we analyze these issues and present the explanation why unitary massive gravitational models, unlike unitary massive electromagnetic ones, cannot coexist from the viewpoint of unitarity with topologically massive terms. We also discuss the novel features of the three-term effective field models that are gauge-invariant.