Argumentation often contains arguments that are themselves argumentations. Representing the general argumentation requires an argumentation model to express the role of an argument as an argumentation and vice versa. Block Argumentation is such an argumentation model intuitively capturing the dual role. However, while modelling in block argumentation is very general, evaluation of acceptability of arguments has not been investigated much. In this paper, we focus on this gap in the literature, and push farther the technical front by presenting a general formulation of acceptability semantics for block argumentation. Specifically, we discuss acceptability semantic issues associated with the generality allowed in block argumentation, identify and characterise two groups of semantic constraints, and formulate acceptability semantics of block argumentation generally with the constraints.