Much work has been done on the study of the biochemical mechanisms that result in ultrasensitive behavior of simple biochemical modules. However, in a living cell, such modules are embedded in a bigger network that constrains the range of inputs that the module will receive as well as the range of the module's outputs that network will be able to detect. Here, we studied how the effective ultrasensitivity of a modular system is affected by these restrictions. We use a simple setup to explore to what extent the dynamic range spanned by upstream and downstream components of an ultrasensitive module impact on the effective sensitivity of the system. Interestingly, we found for some ultrasensitive motifs that dynamic range limitations imposed by downstream components can produce effective sensitivities much larger than that of the original module when considered in isolation.