We measure the Born cross sections of the process e+e-→K+K-K+K- at center-of-mass (c.m.) energies, s, between 2.100 and 3.080 GeV. The data were collected using the BESIII detector at the BEPCII collider. An enhancement at s=2.232 GeV is observed, very close to the e+e-→ΛΛ production threshold. A similar enhancement at the same c.m. energy is observed in the e+e-→φK+K- cross section. The energy dependence of the K+K-K+K- and φK+K- cross sections differs significantly from that of e+e-→φπ+π-.