  NASA's Kepler mission discovered $\sim700$ planets in multi-planet systems
containing 3 or more transiting bodies, many of which are super-Earths and
mini-Neptunes in compact configurations. Using $N$-body simulations, we examine
the in situ, final stage assembly of multi-planet systems via the collisional
accretion of protoplanets. Our initial conditions are constructed using a
subset of the Kepler 5-planet systems as templates. Two different prescriptions
for treating planetary collisions are adopted. The simulations address numerous
questions: do the results depend on the accretion prescription?; do the
resulting systems resemble the Kepler systems, and do they reproduce the
observed distribution of planetary multiplicities when synthetically observed?;
do collisions lead to significant modification of protoplanet compositions, or
to stripping of gaseous envelopes?; do the eccentricity distributions agree
with those inferred for the Kepler planets? We find the accretion prescription
is unimportant in determining the outcomes. The final planetary systems look
broadly similar to the Kepler templates adopted, but the observed distributions
of planetary multiplicities or eccentricities are not reproduced, because
scattering does not excite the systems sufficiently. In addition, we find that
$\sim 1$% of our final systems contain a co-orbital planet pair in horseshoe or
tadpole orbits. Post-processing the collision outcomes suggests they would not
significantly change the ice fractions of initially ice-rich protoplanets, but
significant stripping of gaseous envelopes appears likely. Hence, it may be
difficult to reconcile the observation that many low mass Kepler planets have
H/He envelopes with an in situ formation scenario that involves giant impacts
after dispersal of the gas disc.
