Protein-based therapeutics can activate the adaptive immune system, leading to the production of neutralizing antibodies and the clearance of the treated cells mediated by cytotoxic T cells. Here, we show that the sequential use of immune-orthogonal orthologues of CRISPR-associated protein 9 (Cas9) and adeno-associated viruses (AAVs) evades adaptive immune responses and enables effective gene editing using repeated dosing. We compared total sequence similarities and predicted binding strengths to class-I and class-II major histocompatibility complex (MHC) proteins for 284 DNA-targeting and 84 RNA-targeting CRISPR effectors and 167 AAV VP1-capsid-protein orthologues. We predict the absence of cross-reactive immune responses for 79% of the DNA-targeting Cas orthologues—which we validated for three Cas9 orthologues in mice—yet we anticipate broad immune cross-reactivity among the AAV serotypes. We also show that efficacious in vivo gene editing is uncompromised when using multiple dosing with orthologues of AAVs and Cas9 in mice that were previously immunized against the AAV vector and the Cas9 cargo. Multiple dosing with protein orthologues may allow for sequential regimens of protein therapeutics that circumvent pre-existing immunity or induced immunity.