  The e+e- --> pi+pi-pi0pi0 reaction cross section as a function of the
incident energy is calculated using a model that is an extension of our
recently published model of the e+e- annihilation into four charged pions. The
latter considered the intermediate states with the pi, rho, and a_1 mesons and
fixed the mixing angle of the a_1-rho-pi Lagrangian and other parameters by
fitting the cross section data. Here we supplement the original intermediate
states with those containing omega(782) and h_1(1170), but keep unchanged the
values of those parameters that enter both charged and mixed channel
calculations. The inclusion of omega is vital for obtaining a good fit to the
cross section data, while the intermediate states with h_1 further improve it.
Finally, we merge our models of the e+e- --> pi+pi-pi0pi0 and e+e- -->
pi+pi-pi+pi- reactions and obtain a simultaneous good fit.
