Infrastructural and societal changes intertwine in multiple ways. This makes the societal implications of infrastructural projects difficult to assess and anticipate. Yet in present day network societies this task is particularly urgent. This paper first identifies two positions that tend to monopolize and deadlock debates. Next it examines two decades of research in the Large Technical System (LTS) research field for alternative approaches to this issue, before finally suggesting distinguishing between the four increasingly indirect moments of (co-) construction of infrastructures and societies. These may be related causally, but also add their own moments of contingency, agency, and choice.