Although the brain is often characterized as a complex system, theoretical and philosophical frameworks often struggle to capture this. For example, mainstream mechanistic accounts model neural systems as fixed and static in ways that fail to capture their dynamic nature and large set of possible behaviors. In this paper, we provide a framework for capturing a common type of complex system in neuroscience, which involves two main aspects: (i) constraints on the system and (ii) the system's possibility space of available outcomes. Our analysis merges neuroscience examples with recent work in the philosophy of science to suggest that the possibility space concept involves two essential types of constraints, which we call hard and soft constraints. Our analysis focuses on a domain-general notion of possibility space that is present in manifold frameworks and representations, phase space diagrams in dynamical systems theory, and paradigmatic cases, such as Waddington's epigenetic landscape model. After building the framework with such cases, we apply it to three main examples in neuroscience: adaptability, resilience, and phenomenology. We explore how this framework supports a philosophical toolkit for neuroscience and how it helps advance recent work in the philosophy of science on constraints, scientific explanations, and impossibility explanations. We show how fruitful connections between neuroscience and philosophy can support conceptual clarity, theoretical advances, and the identification of similar systems across different domains in neuroscience.