The primary objectives of this study are to evaluate the safety, tolerability, immunologic noninferiority (for shared serotypes) and immunologic superiority (for novel serotypes) of VAX-31 compared to PCV21 and PCV20 in adults ≥50 years of age, and to bridge the immune responses induced by VAX-31 in adults 50-64 years of age to adults 18-49 years of age.