Multi-Agent AI systems (MAS) have transformative healthcare potentials. However, as a result of different approaches, policies, infrastructural and socio-political challenges, varied applications of MAS have appeared across several countries. This mixed-methods comparative study of MAS application in Nigeria (Lagos) and Russia (Moscow) dives into differing issues such as infrastructural preparedness, legal policies and actual implementation. Whereas Moscow has an advanced healthcare system that employs MAS in telemedicine and preventive medicine, surgeries (such as Da Vinci systems), Lagos implements MAS in diagnosis and EHR (electronic health record system) integration, which could be referred to as foundational applications. This study highlights main adoption challenges, including funding hurdles, gaps in operability and sociocultural resistance, while presenting solutions for improvement- such as FHIR (Fast Healthcare Interoperability Resources) standards in Nigeria and federated learning pilots in Russia. The study further dives into on how government policies, digital literacy, and local innovation ecosystems shape the effectiveness of MAS adoption in both settings. Lagos and Moscow were chosen as case studies as they are national health and economic innovation hubs, and both locations have remarkable models to emulate for new e-healthcare economies. By reviewing outcomes (efficiency, reduced errors) with qualitative insights (methods), this study could prove a suitable blueprint for implementing and optimizing MAS across a plethora of healthcare systems, with a view to a broader African and Eurasian adoption.