The genome of influenza A virus is organized into eight ribonucleoproteins, each composed of a distinct RNA segment bound by the viral polymerase and oligomeric viral nucleoprotein. Packaging sequences unique to each RNA segment together with specific nucleoprotein amino acids are thought to ensure the precise incorporation of these eight ribonucleoproteins into single virus particles, and yet the underlying interaction network remains largely unexplored. We show here that the genome packaging mechanism of an H7N7 subtype influenza A virus widely tolerates the mutation of individual packaging sequences in three different RNA segments. However, combinations of these modified RNA segments cause distinct genome packaging defects, marked by the absence of specific RNA segment subsets from the viral particles. Furthermore, we find that combining a single mutated packaging sequence with sets of specific nucleoprotein amino acid substitutions greatly impairs the viral genome packaging process. Along with previous reports, our data propose that influenza A virus uses a redundant and plastic network of RNA-RNA and potentially RNA-nucleoprotein interactions to coordinately incorporate its segmented genome into virions. IMPORTANCE The genome of influenza A virus is organized into eight viral ribonucleoproteins (vRNPs); this provides evolutionary advantages but complicates genome packaging. Although it has been shown that RNA packaging sequences and specific amino acids in the viral nucleoprotein (NP), both components of each vRNP, ensure selective packaging of one copy of each vRNP per virus particle, the required RNA-RNA and RNA-NP interactions remain largely elusive. We identified that the genome packaging mechanism tolerates the mutation of certain individual RNA packaging sequences, while their combined mutation provokes distinct genome packaging defects. Moreover, we found that seven specific amino acid substitutions in NP impair the function of RNA packaging sequences and that this defect is partially restored by another NP amino acid change. Collectively, our data indicate that packaging of the influenza A virus genome is controlled by a redundant and plastic network of RNA/protein interactions, which may facilitate natural reassortment processes.