This paper introduces a new paradigm for modeling and implementing software artifacts that allows for the separation of overlapping concerns along multiple dimensions of composition and decomposition. The authors argue that existing methodologies and formalisms support only orthogonal separations, leading to well-known problems such as scattering and tangling. The proposed model, called *multi-dimensional separation of concerns*, addresses these issues by introducing *hyperslices* and *hypermodules*. Hyperslices are sets of conventional modules that encapsulate concerns in dimensions other than the dominant one, allowing for simultaneous decomposition along multiple dimensions. Hypermodules are sets of hyperslices with composition rules that specify how they must be composed to form a complete artifact. The paper demonstrates the utility of this model through a case study and discusses its instantiation for specific artifact development formalisms. The authors also review related work, including subject-oriented programming and aspect-oriented programming, highlighting how their approaches can be seen as instantiations of the proposed model.This paper introduces a new paradigm for modeling and implementing software artifacts that allows for the separation of overlapping concerns along multiple dimensions of composition and decomposition. The authors argue that existing methodologies and formalisms support only orthogonal separations, leading to well-known problems such as scattering and tangling. The proposed model, called *multi-dimensional separation of concerns*, addresses these issues by introducing *hyperslices* and *hypermodules*. Hyperslices are sets of conventional modules that encapsulate concerns in dimensions other than the dominant one, allowing for simultaneous decomposition along multiple dimensions. Hypermodules are sets of hyperslices with composition rules that specify how they must be composed to form a complete artifact. The paper demonstrates the utility of this model through a case study and discusses its instantiation for specific artifact development formalisms. The authors also review related work, including subject-oriented programming and aspect-oriented programming, highlighting how their approaches can be seen as instantiations of the proposed model.