Engineered nanobodies (VHs) to the SARS-CoV-2 receptor-binding domain (RBD) were generated using phage display technology. A recombinant Wuhan RBD served as bait in phage panning to fish out nanobody-displaying phages from a VH/VHH phage display library. Sixteen phage-infected E. coli clones produced nanobodies with 81.79-98.96% framework similarity to human antibodies; thus, they may be regarded as human nanobodies. Nanobodies of E. coli clones 114 and 278 neutralized SARS-CoV-2 infectivity in a dose-dependent manner; nanobodies of clones 103 and 105 enhanced the virus's infectivity by increasing the cytopathic effect (CPE) in an infected Vero E6 monolayer. These four nanobodies also bound to recombinant Delta and Omicron RBDs and native SARS-CoV-2 spike proteins. The neutralizing VH114 epitope contains the previously reported VYAWN motif (Wuhan RBD residues 350-354). The linear epitope of neutralizing VH278 at Wuhan RBD 319RVQPTESIVRFPNITN334 is novel. In this study, for the first time, we report SARS-CoV-2 RBD-enhancing epitopes, i.e., a linear VH103 epitope at RBD residues 359NCVADVSVLYNSAPFFTFKCYG380, and the VH105 epitope, most likely conformational and formed by residues in three RBD regions that are spatially juxtaposed upon the protein folding. Data obtained in this way are useful for the rational design of subunit SARS-CoV-2 vaccines that should be devoid of enhancing epitopes. VH114 and VH278 should be tested further for clinical use against COVID-19.