This paper discusses three main topics within the area of generalised near-group fusion categories. \par The first is that of extensions of generalised near-group fusion categories; an example is given with the extension also being a generalised near-group fusion category. It is concluded that all extensions of the Fibonacci category are generalised near-group fusion categories. \par The second concerns what are called slightly degenerate generalised near-group fusion categories. A classification result is given relative to a certain fusion category $\Cal{J}_{N,\zeta}$ defined in a previous work of the authors. \par The third covers the topic of braided generalised Tambara-Yamagami fusion categories. A result here is also given relative to $\Cal{J}_{N,\zeta}$.