Biopolymer syntheses in living cells are perfected by an elaborate error correction machinery, which was not applicable during polymerization on early Earth. Scientists are consequently striving to identify mechanisms by which functional polymers were selected and further amplified from complex prebiotic mixtures. Here we show the instrumental role of non-enzymatic replication in the enrichment of certain product(s). To this end, we analyzed a complex web of reactions in β-sheet peptide networks, focusing on the formation of specific intermediate compounds and template-assisted replication. Remarkably, we find that the formation of several products in a mixture is not critically harmful, since efficient and selective template-assisted reactions serve as a backbone correction mechanism, namely, for keeping the concentration of the peptide containing the native backbone equal to, or even higher than, the concentrations of the other products. We suggest that these findings may shed light on molecular evolution processes that led to current biology.