  We formulate a three-dimensional semi-classical model to treat three-electron
escape dynamics in a strongly-driven linear triatomic molecule, HeH$_{2}^{+}$.
Our model includes the Coulomb singularities. Hence, to avoid unphysical
autoionization, we employ two criteria to switch off the Coulomb repulsive
force between two bound electrons and switch it on when the motion of one
electron is mostly determined by the laser field. We investigate triple and
"frustrated" triple ionization. In the latter process two electrons escape
while one electron remains bound in a Rydberg state. We find that two pathways
prevail in "frustrated" triple ionization, as in "frustrated" double
ionization. We also find that the electron that remains in a Rydberg state is
more likely to be attached to He$^{2+}$ compared to H$^{+}$. Our results
indicate that in triple and "frustrated" triple ionization electronic
correlation is weak. Moreover, we compute the sum of the kinetic energies as
well as the angular patterns of the final ion fragments in triple and
"frustrated" triple ionization. These patterns suggest that the fragmenting
molecule deviates from its initial linear configuration.
