Gravitational microlensing provides a unique opportunity to probe the mass distribution of stars, black holes, and other objects in the Milky Way. Population simulations are necessary to interpret results from microlensing surveys. The contribution from binary objects is often neglected or minimized in analysis of observations and simulations despite the high percentage of binary systems and microlensing's ability to probe binaries. To simulate the population effects, we added multiple systems to Stellar Population Interface for Stellar Evolution and Atmospheres (SPISEA), which simulates stellar clusters. We then inject these multiples into Population Synthesis for Compact-object Lensing Events (PopSyCLE), which simulates Milky Way microlensing surveys. When making OGLE observational selection criteria, we find that 55% of observed microlensing events involve a binary system. Specifically, 14.5% of events have a multiple lens and a single source, 31.7% have a single lens and a multiple source, and 8.8% have a multiple lens and a multiple source. The majority of these events have photometric light curves that appear single and are fit well by a single-lens, single-source model. This suggests that binary source and binary lens−binary source models should be included more frequently in event analysis. The mean Einstein crossing time shifts from 19.1 days for single events only to 21.3 days for single and multiple events, after cutting binary events with multiple peaks. The Einstein crossing time distribution of single and single-peaked multiple events is better aligned with observed distributions from OGLE than singles alone, indicating that multiple systems are a significant missing piece between simulations and reality.