Temporally varying selection is considered to be one of the potential mechanisms of recombination evolution. We found earlier that simple cyclical selection for a trait controlled by multiple additive, dominant or semi-dominant loci can result in extremely complex limiting behaviour (CLB) of population trajectories, including ‘supercycles’ and more complex attractors. Recombination rate proved to be a key factor affecting the mode of CLB and the very existence of CLB. Therefore, we considered here a generalized model: the fixed recombination rate was replaced by a polymorphic recombination modifier. The modifier-dependent changes included: (a) supercyclical dynamics due to the recombination modifier in a system that does not manifest CLB when recombination rate is a fixed parameter; (b) appearance of a new level of superoscillations (super-supercycles) in a system that manifests supercycles with a fixed modifier; (c) chaotization of the regular supercyclical dynamics. The domain of attraction of these movements appeared to be quite large. It is noteworthy that the modifier locus is an active participant in the observed non-monotonic limiting movements. Interactions between short-period forced oscillations and the revealed long-period auto-oscillations appeared to result in new regimes of recombination evolution (for some range of linkage between the modifier locus and the selected system), as compared with those caused by the forced oscillations alone.