  We measure the Born cross sections of the process $e^{+}e^{-} \to
K^{+}K^{-}K^{+}K^{-}$ at center-of-mass (c.m.) energies, $\sqrt{s}$, between
2.100 and 3.080 GeV. The data were collected using the BESIII detector at the
BEPCII collider. An enhancement at $\sqrt{s}= 2.232$ GeV is observed, very
close to the $e^{+}e^{-} \to \Lambda \overline{\Lambda}$ production threshold.
A similar enhancement at the same c.m. energy is observed in the $e^{+}e^{-}
\to \phi K^{+}K^{-}$ cross section. The energy dependence of the
$K^{+}K^{-}K^{+}K^{-}$ and $\phi K^{+}K^{-}$ cross sections differs
significantly from that of $e^{+}e^{-} \to \phi \pi^{+}\pi^{-}$.
