Despite ongoing efforts in cancer research, a fully effective treatment for glioblastoma multiforme (GBM) is still unknown. Since adoptive cell transfer immunotherapy is one of the potential cure candidates, efforts have been made to assess its effectiveness using mathematical modeling. In this paper, we consider a model of GBM immunotherapy proposed by Abernathy and Burke (2016), which also takes into account the dynamics of cancer stem cells, i.e., the type of cancer cells that are hypothesized to be largely responsible for cancer recurrence. We modify the initial ODE system by applying simplifying assumptions and analyze the existence and stability of steady states of the obtained simplified model depending on the treatment levels.