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We develop a two-stage computational method to assimilate linear viscoelastic material functions (LMFs), viz., stress relaxation modulus, creep compliance, and the complex modulus, by inferring a consensus discrete relaxation spectrum (DRS) that simultaneously fits all three LMFs. In the first stage, the DRS corresponding to the different LMFs is deduced independently, before they are combined heuristically to generate an initial guess for the consensus DRS. In the second stage, this initial guess is refined using nonlinear least squares regression. The effectiveness of this method for data fusion and validation is demonstrated by analyzing experimental data collected on two different polymer melt systems. We also investigate the performance of the method when the timescales probed by the LMFs do not overlap, or are limited to 4–6 decades, as is typically the case for thermorheologically complex materials. To explore these questions, we generate synthetic datasets by obscuring information from one of the experimental datasets. We find that the computational protocol works quite well. As expected, the quality of the inferred DRS is marginally impaired because information is suppressed.