Following up on our previous review paper ‘Review of manufacturing system design in the interplay of Industry 4.0 and Industry 5.0 (Part I): Design thinking and modeling methods’ [1], based on the proposed Thinking-Modelling-Process-Enabler (TMPE) framework of Manufacturing System Design (MSD), this paper (Part II of the two-part review) further reviews the Process and Enabler dimensions of MSD in the interplay of Industry 4.0 and Industry 5.0. MSD methods are reviewed from the single-dimensional design process and cross-dimensional design process perspectives, respectively. MSD methods are reorganized and categorized from the key enabler's perspective. Finally, challenges are discussed along with directions for future research in the domain of MSD. This review is anticipated to offer novel insights for advancing MSD research and engineering in the interplay of Industry 4.0 and Industry 5.0.