Human influenza A virus (IAV) vaccination is limited by "antigenic drift," rapid antibody-driven escape reflecting amino acid substitutions in the globular domain of hemagglutinin (HA), the viral attachment protein. To better understand drift, we used anti-hemagglutinin monoclonal Abs (mAbs) to sequentially select IAV escape mutants. Twelve selection steps, each resulting in a single amino acid substitution in the hemagglutinin globular domain, were required to eliminate antigenicity defined by monoclonal or polyclonal Abs. Sequential mutants grow robustly, showing the structural plasticity of HA, although several hemagglutinin substitutions required an epistatic substitution in the neuraminidase glycoprotein to maximize growth. Selecting escape mutants from parental versus sequential variants with the same mAb revealed distinct escape repertoires, attributed to contextual changes in antigenicity and the mutation landscape. Since each hemagglutinin mutation potentially sculpts future mutation space, drift can follow many stochastic paths, undermining its unpredictability and underscoring the need for drift-insensitive vaccines.