The purpose of this article is to develop a conceptual framework clarifying how firms behaviourally venture or risk through entrepreneurial innovation (EI), in the ‘contexts’ of globalisation, society, innovation users or public perceptions; we methodologically coined these ‘contexts’ as ‘4-GSIP variables’ and applied them in that order. We then examined EI literature and built on variants of its theoretical insights to describe conceptual frameworks of how innovation focus firms behaviourally deal with the contextual implications of the variables. Our frameworks also show how firms contextually and behaviourally venture through EI in line with the variables. Findings indicate that firms’ EI behaviour varies or differs across contexts (the variables) yet shared to an extent. Also, firms’ innovation behaviour is shaped by its external environment (the variables). We concluded that firms behaviourally risk through innovation by collaborating with the external variables to ensure responsible or sustainable innovations.