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 Frevertants 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.