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We investigate aspects of universality in the two-dimensional (2D) spin-1 Baxter-Wu model in a crystal field Δ using a parallel version of the multicanonical algorithm employed at constant temperature T. A detailed finite-size scaling analysis in the continuous regime of the Δ – T phase diagram of the model indicates that the transition belongs to the universality class of the 4-state Potts model. The presence of first-order-like finite-size effects that become more pronounced as one approaches the pentacritical point of the model is highlighted and discussed.