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In 2005 Gilkey and Nik\v cevi\'c introduced complete $(p+2)$-curvature homogeneous pseudo-Rie\-mannian manifolds of neutral signature $(3 + 2p, 3 + 2p)$, which are $0$-modeled on an indecomposable symmetric space, but which are not $(p + 3)$-curvature homogeneous. In this paper the authors continue their study of the same family of manifolds by examining their isometry groups and the isometry groups of their $k$-models.
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