  The non-extensive statistical description of the identified final state
particles measured in high energy collisions is well-known by its wide range of
applicability. However, there are many open questions that need to be answered,
including but not limited to, the question of the observed mass scaling of
massive hadrons or the size and multiplicity dependence of the model
parameters. This latter is especially relevant, since currently the amount of
available experimental data with high multiplicity at small systems is very
limited. This contribution has two main goals: On the one hand we provide a
status report of the ongoing tuning of the soon-to-be-released HIJING++ Monte
Carlo event generator. On the other hand, the role of multiplicity dependence
of the parameters in the non-extensive hadronization model is investigated with
HIJING++ calculations. We present cross-check comparisons of HIJING++ with
existing experimental data to verify its validity in our range of interest as
well as calculations at high-multiplicity regions where we have insufficient
experimental data.
