Triple helix collaborations are evidence and example of larger 'post-postmodern' trends that have accelerated the convergence of once clearly established organisational dichotomies, in particular, market/hierarchy, private/public and for-profit/non-profit. The multiplex hybridity of triple helix collaborations creates unique challenges for the functional and, in particular, advance legal organisation and governance of their social welfare-oriented, quasi-entrepreneurial, quasi-regulatory innovation interactivity. Social innovation, resource valorisation and sustainability-constituting core normative underpinnings and objectives for triple helix models-similarly affect the design and efficiency of hybrid firms that functionally and legally domicile triple helix intermediation. In an effort to help promote the emergence of sui-generis best practices in the intermediation of 'innovation in innovation' (Etzkowitz, Stud Sci 42(3):293-337, 2003a) triple helix projects, this article focuses on two interrelated aspects of triple helix hybridity which are less developed in the current literatures: First, based on a well-documented case study of a failed research group-firm hybrid within the University of Helsinki, it examines an institutionalised supra-helical, fourth-party intermediation model for triple helix networks and distinguishes such theoretical model from mere inter-helical self-intermediation in trilateral university-industry-government collaborations. Second, it hypothesises the possible association of supra-helical, fourth-party triple helix intermediation in application with blended private/public, for-profit/non-profit legal entities, in particular, only recently introduced hybrid legal organisations in the UK, the USA, and Canada. The main thesis developed under such dual focus is that the unique legal organisational design and domicile for triple helix intermediation, i.e. what this article terms the supra-helical mode 3 substructure, critically matters-both, for purposes of institutionalising efficient decision-making and governance equilibria in the promotion and operation of real-world triple helix projects and for controlling the agency and social costs of such advanced triple helix collaborations.