Targeted genome editing using engineered nucleases facilitates the creation of bona fide cellular models for biological research and may be applied to human cell-based therapies. Broadly applicable and versatile methods for increasing the levels of gene editing in cell populations remain highly desirable due to the variable efficiency between distinct genomic loci and cell types. Harnessing the multiplexing capabilities of CRISPR-Cas9 and Cpf1 systems, we designed a simple and robust co-selection strategy for enriching cells harboring either nuclease-driven non-homologous end joining (NHEJ) or homology-directed repair (HDR) events. Selection for dominant alleles of the endogenous sodium-potassium pump (Na+,K+-ATPase) that render cells resistant to ouabain is used to enrich for custom modifications at another unlinked locus of interest, effectively increasing the recovery of engineered cells. The process was readily adaptable to transformed and primary cells, including hematopoietic stem and progenitor cells (HSPCs). The use of universal CRISPR reagents and a commercially available small molecule inhibitor streamlines the incorporation of marker-free genetic changes in human cells.