The present paper offers a more macroscopic and system-oriented analysis of the tense-taxis-aspect-mood (TTAM) semantics of the Biblical Hebrew verbal system developed within the framework of grammaticalization-based maps and cognitive linguistics. By combining the maps (i.e. qualitative compositions of senses) and waves (i.e. qualitative-quantitative complexes of senses) into higher-level dynamic modules, i.e. currents, and by explaining the global system in terms of such currents, the study designs a possible way of expansion of the semantic maps’ model from a gram-oriented analysis to a more systemic perspective. Accordingly, higher level properties of the sub-modules of the Biblical Hebrew verbal system are postulated, the environments of grams are expanded from their immediate setting (the adjacent waves on the stream) to other, more distant, regions of the verbal organization, and a tentative dynamic model of the entire Biblical Hebrew verbal system is formulated.