The main international IT Service Management processes frameworks (ITIL v2, ISO/IEC 20000, COBIT 4.0, CMMI-SVC, MOF 4.0, and ITUP) include the design of IT services as part of their main best practices. However, despite having a common purpose and conceptual structure, they are organized differently. Hence, ITSM academic researchers and practitioners need to integrate a broad and diverse literature in relation to these frameworks. In Part I of this research, the authors pursued the goal of a descriptive-comparative analysis of fundamental concepts and IT service architecture design models used in the seven ITSM frameworks. In this paper (Part II) we complete this systemic analysis by using the ISO/IEC 15288 systems engineering standard and focusing on the IT design processes and practices reported in the aforementioned ITSM frameworks. Specifically, CMMI-SVC and ITUP are assessed in overall as the strongest frameworks from an engineering view, MOF 4.0 and ITIL v3 as moderate, and ISO/IEC 20000, ITIL v2 and COBIT as the weakest. ITSM academicians and in particular practitioners thus will need to distinguish their utilization according to the level of required detail of the IT service design process. This paper aims to advance our comprehension and understanding on the state of the art regarding what are IT services and how they can be designed. Thus it is of broad significance to ITSM researchers and practitioners.