The antigenic and genomic stability of paramyxoviruses remains a mystery. Here, we evaluate the genetic plasticity of Sendai virus (SeV) and mumps virus (MuV), sialic acid-using paramyxoviruses that infect mammals from two Paramyxoviridae subfamilies (Orthoparamyxovirinae and Rubulavirinae). We performed saturating whole-genome transposon insertional mutagenesis, and identified important commonalities: disordered regions in the N and P genes near the 3' genomic end were more tolerant to insertional disruptions; but the envelope glycoproteins were not, highlighting structural constraints that contribute to the restricted antigenic drift in paramyxoviruses. Nonetheless, when we applied our strategy to a fusion-defective Newcastle disease virus (Avulavirinae subfamily), we could select for F-revertants and other insertants in the 5' end of the genome. Our genome-wide interrogation of representative paramyxovirus genomes from all three Paramyxoviridae subfamilies provides a family-wide context in which to explore specific variations within and among paramyxovirus genera and species. Author summary: RNA viruses are known for their genetic variability. They often exhibit significant genetic diversity even within members of a given viral species. Paramyxoviruses are notable exceptions. They show relatively little genomic or antigenic change over time. This is exemplified by mumps and measles viruses, where vaccine strains have not been changed in 40 years and still remain effective. Here, we sought to understand the determinants of this relative stability by probing three different paramyxoviruses: Sendai, mumps, and Newcastle disease viruses. We used a mutagenesis strategy to create 15-nucleotide insertions that were randomly distributed across the entire genome. The insertions were designed to identify regions of the viral genome that can or cannot tolerate. After rescuing each of these libraries, we passaged each virus in cell culture twice, and deep sequenced viral RNA from each step to monitor the enrichment or depletion of insertions throughout the genome. In this way, we found that paramyxoviruses displayed an increased tolerance for insertions in proteins with disordered regions, and in the un-translated regions of highly expressed genes. Importantly, we also determined that paramyxoviral structural proteins, which are the most antigenic proteins, do not tolerate insertions, which provides an explanation for why paramyxoviruses are antigenically stable in the face of adaptive immune pressure. Thus, we here provide evidence that constraints on paramyxoviral protein functions contribute to the viruses' genetic stability. [ABSTRACT FROM AUTHOR]