This v.3, in addition to: (a) discussion of the role of constants (called fundamental until 2015) in the proposed New SI formulation of the definition of the International System of Units, namely in the present official documents and in some relevant literature. The meaning assigned to the use of constants is found substantially different even among the advocates of the proposal; (b) focusing on how the stipulation of their numerical values is obtained, according to the specific features of measurement units, arising some special problems, not all cleared yet, that the stipulation of a fundamental constant can place when it becomes part of the definition of the New SI and of a base unit of it. Some reasons are discussed why it is urgent that these basic issues are clarified; (c)in the Appendix, a specific critical review is now added of the text of Sections 1 and 2 of the CCU 2016 Draft, the last implementation of the New SI for the 9th Brochure on the SI, published on the BIPM website on January 4, 2016, and now under examination by the SI top stakeholders. Though this draft is advanced with respect to the CCU 2013 Draft, it is shown how the description of the complex structure of the new definition may still be difficult to be clearly caught even by informed readers, while most users might be lost about their tasks needed to implement the new definition.