Cross section measurements of ${e}^{+}{e}^{-}\to {K}^{+}{K}^{-}{K}^{+}{K}^{-}$ and $\varphi {K}^{+}{K}^{-}$ at center-of-mass energies from 2.10 to 3.08 GeV

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 $\sqrt{s}=2.232\text{}\text{}\mathrm{GeV}$ 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 ${e}^{+}{e}^{-}\to \varphi {K}^{+}{K}^{-}$ cross section. The energy dependence of the ${K}^{+}{K}^{-}{K}^{+}{K}^{-}$ and $\varphi {K}^{+}{K}^{-}$ cross sections differs significantly from that of ${e}^{+}{e}^{-}\to \varphi {\pi }^{+}{\pi }^{-}$.