Developing a model for a signalling pathway requires several iterations of experimentation and model refinement to obtain an accurate model. However, the implementation of such an approach to model a signalling pathway induced by a poorly-known stimulus can become labour intensive because only limited information on the pathway is available beforehand to formulate an initial model. Therefore, a large number of iterations are required since the initial model is likely to be erroneous. In this work, a numerical scheme is proposed to construct a time-varying model for a signalling pathway induced by a poorly-known stimulus when its nominal model is available in the literature. Here, the nominal model refers to one that describes the signalling dynamics under a well-characterised stimulus. First, global sensitivity analysis is implemented on the nominal model to identify the most important parameters, which are assumed to be piecewise constants. Second, measurement data are clustered to determine temporal subdomains where the parameters take different values. Finally, a least-squares problem is solved to estimate the parameter values in each temporal subdomain. The effectiveness of this approach is illustrated by developing a time-varying model for NF-[inline-formula removed]B signalling dynamics induced by lipopolysaccharide in the presence of brefeldin A.