  With a view to computing fluctuation identities related to stable processes,
we review and extend the class of hypergeometric L\'evy processes explored in
Kuznetsov and Pardo (arXiv:1012.0817). We give the Wiener-Hopf factorisation of
a process in the extended class, and characterise its exponential functional.
Finally, we give three concrete examples arising from transformations of stable
processes.
