All lowest-order amplitudes for e+e- --> 4f+gamma are calculated including five anomalous quartic gauge-boson couplings that are allowed by electromagnetic gauge invariance and the custodial SU(2)_c symmetry. Three of these anomalous couplings correspond to the operators L_0, L_c, and L_n that have been constrained by the LEP collaborations in WWgamma production. The anomalous couplings are incorporated in the Monte Carlo generator RACOONWW. Moreover, for the processes e+e- --> 4f+gamma RACOONWW is improved upon including leading universal electroweak corrections such as initial-state radiation. The discussion of numerical results illustrates the size of the leading corrections as well as the impact of the anomalous quartic couplings for LEP2 energies and at 500GeV.