The opioid crisis is transitioning to a polydrug crisis, and individuals with co-occurring substance use disorder (SUDs) often have unique clinical characteristics and contextual barriers that influence treatment needs, engagement in treatment, complexity of treatment planning, and treatment retention. Using Medicaid data for 2017-2018 from four states participating in a distributed research network, this retrospective cohort study documents the prevalence of specific types of co-occurring SUD among Medicaid enrollees with an opioid use disorder (OUD) diagnosis, and assesses the extent to which different SUD presentations are associated with differential patterns of MOUD and psychosocial treatments. We find that more than half of enrollees with OUD had a co-occurring SUD, and the most prevalent co-occurring SUD was for "other psychoactive substances", indicated among about one-quarter of enrollees with OUD in each state. We also find some substantial gaps in MOUD treatment receipt and engagement for individuals with OUD and a co-occurring SUD, a group representing more than half of individuals with OUD. In most states, enrollees with OUD and alcohol, cannabis, or amphetamine use disorder are significantly less likely to receive MOUD compared to enrollees with OUD only. In contrast, enrollees with OUD and other psychoactive SUD were significantly more likely to receive MOUD treatment. Conditional on MOUD receipt, enrollees with co-occurring SUDs had 10 % to 50 % lower odds of having a 180-day period of continuous MOUD treatment, an important predictor of better patient outcomes. Associations with concurrent receipt of MOUD and behavioral counseling were mixed across states and varied depending on co-occurring SUD type. Overall, ongoing progress toward increasing access to and quality of evidence-based treatment for OUD requires further efforts to ensure that individuals with co-occurring SUDs are engaged and retained in effective treatment. As the opioid crisis evolves, continued changes in drug use patterns and populations experiencing harms may necessitate new policy approaches that more fully address the complex needs of a growing population of individuals with OUD and other types of SUD.