Social relationships have a strong influence on individual travel behavior and, consequently, on travel demand. However, most current literatures on population synthesis, which is the fundamental building block of disaggregated travel demand forecasting and agent-based traffic simulation, only considers the household impact. This paper makes two contributions in this regard. First, a methodological issue is identified: the existence of multiple social relationships (e.g., a dual set of constraints from social institutions or structures) makes it more difficult to generate a consistent synthetic population, meaning that this population satisfies constraints from more than one type of social organizations. A tensor decomposition method is then proposed to generate a consistent population with multi-social relationships. To our knowledge, this is the first time that this type of methodological issue has been addressed. Our sample-based method constitutes an improvement compared to existing approaches in that it can respect constraints from multiple social organizations without reducing accuracy. A numerical test concerning individual, household, and enterprise, using Chinese national population and economic census data, indicates that the new method can lead to stable and relatively small errors in total. The source code is available from https://github.com/PeijunYe/MulSocPopSyn.git.