The emergence of SARS-CoV-2 recombinants is of particular concern as they can result in a sudden increase in immune evasion due to antigenic shift. Recent recombinants XBB and XBB.1.5 have higher transmissibility than previous recombinants such as "Deltacron." We hypothesized that immunity to a SARS-CoV-2 recombinant depends on prior exposure to its parental strains. To test this hypothesis, we examined whether Delta or Omicron (BA.1 or BA.2) immunity conferred through infection, vaccination, or breakthrough infection could neutralize Deltacron and XBB/XBB.1.5 recombinants. We found that Delta, BA.1, or BA.2 breakthrough infections provided better immune protection against Deltacron and its parental strains than did the vaccine booster. None of the sera were effective at neutralizing the XBB lineage or its parent BA.2.75.2, except for the sera from the BA.2 breakthrough group. These results support our hypothesis. In turn, our findings underscore the importance of multivalent vaccines that correspond to the antigenic profile of circulating variants of concern and of variant-specific diagnostics that may guide public health and individual decisions in response to emerging SARS-CoV-2 recombinants.