  We report the first observation of multiple intercommutation (more than two
successive reconnections) of cosmic strings at ultra-high collision speeds, and
the formation of ``kink trains'' with up to four closely spaced left- or
right-moving kinks. We performed a flat space numerical study of abelian Higgs
cosmic string intercommutation in the type-II regime $\beta > 1$ (where $\beta
= m^2_{scalar} / m^2_{gauge}$) up to $\beta = 64$, the highest value
investigated to date. Our results confirm earlier claims that the minimum
critical speed for double reconnection goes down with increasing $\beta$, from
$\sim 0.98 c$ at $\beta = 1$ to $\sim 0.86 c$ for $\beta = 64$. Furthermore, we
observe a qualitative change in the process leading to the second
intercommutation: if $\beta \geq 16$ it is mediated by a loop expanding from
the collision point whereas if $1 < \beta \leq 8 $ the previously reported
``loop'' is just an expanding blob of radiation which has no topological
features and is absorbed by the strings. The multiple reconnections are
observed in the loop-mediated, deep type-II regime $\beta \geq 16$. Triple
reconnections appear to be quite generic for collision parameters on the
boundary between single and double reconnection. For $\beta = 16$ we observe
quadruple events. They result in clustering of small scale structure in the
form of ``kink trains''. Our findings suggest that, due to the core
interactions, the small scale structure and stochastic gravitational wave
background of abelian Higgs strings in the strongly type-II regime may be quite
different from what would be expected from studies of Nambu-Goto strings or of
abelian Higgs strings in the $\beta \approx 1$ regime.
