The hemagglutinin (HA) stem region is a major target of universal influenza vaccine efforts owing to the presence of highly conserved epitopes across multiple influenza A virus (IAV) strains and subtypes. To explore the potential impact of vaccine-induced immunity targeting the HA stem, we examined the fitness effects of viral escape from stem-binding broadly neutralizing antibodies (stem-bnAbs). Recombinant viruses containing each individual antibody escape substitution showed diminished replication compared to wild-type virus, indicating that stem-bnAb escape incurred fitness costs. A second-site mutation in the HA head domain (N129D; H1 numbering) reduced the fitness effects observed in primary cell cultures and likely enabled the selection of escape mutations. Functionally, this putative permissive mutation increased HA avidity for its receptor. These results suggest a mechanism of epistasis in IAV, wherein modulating the efficiency of attachment eases evolutionary constraints imposed by the requirement for membrane fusion. Taken together, the data indicate that viral escape from stem-bnAbs is costly but highlights the potential for epistatic interactions to enable evolution within the functionally constrained HA stem domain.