Experiences are reported in the use of ISO 15504 both in tailoring the standard for particular industrial sectors and in expanding the process assessment approach into new domains. In particular, three projects are discussed: $\bullet $SPiCE for SPACE, a ISO/IEC TR 15504 [IS98a] conformant method of software process assessment developed for the European space industry, $\bullet $SPiCE-9000 for SPACE, an assessment method for space quality management systems, based on ISO 9001:2000 [IS00], and $\bullet $NOVE-IT, a project of the Swiss federal government to establish and assess processes covering IT procurement, development, operation, and service provision. All three of these projects use the concepts of process assessment from ISO 15504; however, in each case, different strategies to apply the international standard were selected. Some of the issues faced in these different domains are described and their resolutions presented.