The KTeV experiment at Fermilab has isolated a total of 132 events from the rare decay K(L)-->e+ e- mu+ mu-, with an estimated background of 0.8 events. The branching ratio of this mode is determined to be [2.69+/-0.24(stat)+/-0.12(syst)]x10(-9), with a radiative cutoff of M(2)(ee mu mu)/M(2)(K)>0.95. The first measurement using this mode of the parameter alpha from the D'Ambrosio-Isidori-Portolès (DIP) model of the K(L)gamma*gamma* vertex yields a result of -1.59+/-0.37, consistent with values obtained from other decay modes. Because of the limited statistics, no sensitivity is found to the DIP parameter beta. We use this decay mode to set limits on CP and lepton violation.