The measles virus (MV) is serologically monotypic. Life-long immunity is conferred by a single attack of measles or following vaccination with the MV vaccine. This is contrary to viruses such as influenza, which readily develop resistance to the immune system and recur. A better understanding of factors that restrain MV to one serotype may allow us to predict if MV will remain monotypic in the future and influence the design of novel MV vaccines and therapeutics. MV hemagglutinin (H) glycoprotein, binds to cellular receptors and subsequently triggers the fusion (F) glycoprotein to fuse the virus into the cell. H is also the major target for neutralizing antibodies. To explore if MV remains monotypic due to a lack of plasticity of the H glycoprotein, we used the technology of Immune Dampening to generate viruses with rationally designed N-linked glycosylation sites and mutations in different epitopes and screened for viruses that escaped monoclonal antibodies (mAbs). We then combined rationally designed mutations with naturally selected mutations to generate a virus resistant to a cocktail of neutralizing mAbs targeting four different epitopes simultaneously. Two epitopes were protected by engineered N-linked glycosylations and two epitopes acquired escape mutations via two consecutive rounds of artificial selection in the presence of mAbs. Three of these epitopes were targeted by mAbs known to interfere with receptor binding. Results demonstrate that, within the epitopes analyzed, H can tolerate mutations in different residues and additional N-linked glycosylations to escape mAbs. Understanding the degree of change that H can tolerate is important as we follow its evolution in a host whose immunity is vaccine induced by genotype A strains instead of multiple genetically distinct wild-type MVs.