The multicritical behavior of the Blume-Capel model with infinite-range interactions is investigated by introducing quenched disorder in the crystal field Δi, which is represented by a superposition of two Gaussian distributions with the same width σ, centered at Δi = Δ and Δi = 0, with probabilities p and (1 - p), respectively. A rich variety of phase diagrams is presented, and their distinct topologies are shown for different values of σ and p. The tricritical behavior is analyzed through the existence of fourth-order critical points, as well as how the complexity of the phase diagrams is reduced by the strength of the disorder. © 2010 IOP Publishing Ltd.