  Suprathermal electrons and inertial drifting electrons, so called electron
beam, are crucial to the nonlinear dynamics of electrostatic solitary waves
observed in several astrophysical plasmas. In this paper, the propagation of
electron-acoustic solitary waves is investigated in a collisionless,
unmagnetized plasma consisting of cool inertial background electrons, hot
suprathermal electrons (modeled by a $\kappa$-type distribution), and
stationary ions. The plasma is penetrated by a cool electron beam component. A
linear dispersion relation is derived to describe small-amplitude wave
structures that shows a weak dependence of the phase speed on the electron beam
velocity and density. A (Sagdeev-type) pseudopotential approach is employed to
obtain the existence domain of large-amplitude solitary waves, and investigate
how their nonlinear structures depend on the kinematic and physical properties
of the electron beam and the suprathermality (described by $\kappa$) of the hot
electrons. The results indicate that the electron beam can largely alter the
electron-acoustic solitary waves, but can only produce negative polarity
solitary waves in this model. While the electron beam co-propagates with the
solitary waves, the soliton existence domain (Mach number range) becomes
narrower (nearly down to nil) with increasing the beam speed and the
beam-to-hot electron temperature ratio, and decreasing the beam-to-cool
electron density ratio in high suprathermality (low $\kappa$). It is found that
the electric potential amplitude largely declines with increasing the beam
speed and the beam-to-cool electron density ratio for co-propagating solitary
waves, but is slightly decreased by raising the beam-to-hot electron
temperature ratio.
