Minor (5-10 fold) activation of mitogenic signalling cascades typically induces cell division upon extracellular stimulation and is sufficient to support tumourigenesis when permanently triggered by activating mutations. Surprisingly, even strong signalling protein overexpression usually does not trigger deregulated cell proliferation, suggesting that basal state signalling is insensitive to wildtype protein overexpression. Using kinetic modelling of the core Ras cycle, we show that basal RasGTP signalling can be insensitive to Ras overexpression and thus identify a possible tumour suppression mechanism. We further show how phenotypically silent overexpression events within signalling cascades cooperate to bring about carcinogenesis. Our analyses underscore the need for a systems level understanding of tumour formation.