Blockchain is a very attractive technology since it maintains a public, append-only, immutable and ordered log of transactions which guarantees an auditable ledger accessible by anyone. Blockchain systems are inherently interdisciplinary since they combine various fields such as cryptography, multi-agent systems, distributed systems, social systems, economy, and finance. Furthermore, they have a very active and dynamic ecosystem where new blockchain platforms and algorithms are developed continuously due to the interest of the public and the industries to the technology. Consequently, we anticipate a challenging and interdisciplinary research agenda in blockchain systems, built upon a methodology that strives to capture the rich process resulting from the interplay between the behavior of agents and the dynamic interactions among them. To be effective, however, modeling studies providing insights into blockchain systems, and appropriate description of agents paired with a generic understanding of their components are needed. Such studies will create a more unified field of blockchain systems that advances our understanding and leads to further insight. According to this perspective, in this study, we propose using a generic multi-agent organizational modeling for studying blockchain systems, namely AGR4BS. Concretely, we use the Agent/Group/Role (AGR) organizational modeling approach to identify and represent the generic entities which are common to blockchain systems. We show through four real case studies how this generic model can be used to model different blockchain systems. We also show briefly how it can be used for modeling three well-known attacks on blockchain systems.