Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) continues to evolve, escape coronavirus disease 2019 therapeutics and vaccines, and jeopardize public health. To combat SARS-CoV-2 antigenic escape, we developed a rapid, high-throughput pipeline to discover monospecific VHH antibodies and iteratively develop VHH-Fc-VHH bispecifics capable of neutralizing emerging SARS-CoV-2 variants. By panning VHH single-domain phage libraries against ancestral or beta spike proteins, we discovered high-affinity VHH antibodies with unique target epitopes. Combining two VHHs into a tetravalent bispecific construct conferred broad neutralization activity against multiple variants and was more resistant to antigenic escape than the monospecific antibody alone. Following the rise of the Omicron variant, a VHH in the original bispecific construct was replaced with another VHH discovered against the Omicron BA.1 receptor binding domain; the resulting bispecific exhibited neutralization against both BA.1 and BA.5 sublineage variants. A heavy chain-only tetravalent VHH-Fc-VHH bispecific platform derived from humanized synthetic libraries held a myriad of unique advantages: (i) synthetic preconstructed libraries minimized risk of liabilities and maximized discovery speed, (ii) VHH scaffolds allowed for a modular "plug-and-play" format that could be rapidly iterated upon as variants of concern arose, (iii) natural dimerization of single VHH-Fc-VHH polypeptides allowed for straightforward bispecific production and purification methods, and (iv) multivalent approaches enhanced avidity boosting effects and neutralization potency, and conferred more robust resistance to antigenic escape than monovalent approaches against specific variants. This iterative platform of rapid VHH discovery combined with modular bispecific design holds promise for long-term viral control efforts.