The essay considers the role of big private businesses (BBs) within the Brazilian national system of innovation (NSI). Our question is as follows: How do the innovation practices and political behavior adopted by BBs shape the Brazilian NSI? It is our claim that although BBs play a prominent role in leading innovation nationally, they are not supportive of institution-intensive solutions for strengthening the NSI, and thereby contribute to the creation of a dynamic that we call the ‘low-innovation trap’. The obstacles to escaping this trap are manifold, but here we shall focus on 01. the lack of coordination between actors and instruments within government, 02. the high level of instability in the Science, Technology and Innovation (ST&I) budget, 03. the increasing obstacles faced by BBs wishing to innovate and 04. the lack of correspondence between government proposals and societal demands. Without a strong coalition pushing for it to be upgraded, it is likely that the NSI will remain unfit for purpose.