A two-step quench process is modeled using Cahn-Hilliard theory for symmetric binary polymer mixtures. The blend is quenched from a stable state in the one-phase region to an unstable state in the two-phase region where it undergoes spinodal decomposition. The mixture is allowed to coarsen for two different time periods before a second quench was applied to a point further inside the unstable region. During the initial stages following the second quench smaller secondary domains appeared briefly in the primary domains obtained from the first quench step. The peak arising from the second quench step was isolated from the structure factor, and the early growth stages were investigated using linearized theory. We also quantify the maximum degree of secondary phase separation as a function of quench depth, which we hope will provide stimulus for further experimental studies.