In this review, we discuss empirical results inspiring the introduction of a formal mathematical multilayer model for the biological neuroscience of conscious experience. First, we motivate the discussion through evidence regarding the dynamic brain. Second, we review different brain-body couplings associated with conscious experience and its potential role in driving brain dynamics. Third, we introduce the machinery of multilayer networks to account for several types of interactions in brain-body systems. Then, a multilayer structure consists of two main generalisations: a formal semantic to study biological systems, and an integrative account for several signatures and models of consciousness. Finally, under this framework, we define composition of layers to account for entangled features of brain-body systems related to conscious experience. As such, a multilayer mathematical framework is highly integrative and thus may be more complete than other models.