“Multiglass” materials with simultaneous occurrence of two different glassy states extend the frame of conventional multiferroicity, which is devoted to crystalline materials with coexisting uniform long-range electric and magnetic ordering. The concept applies to Sr0.98Mn0.02TiO3 ceramics, where A-site substituted Mn2+ ions are at the origin of both a polar and a spin cluster glass. Spin freezing is initiated below the dipolar glass temperature, Tg e ≈ 38 K, which is seemingly indicated by a divergence of the nonlinear susceptibility, χ3. Below Tg m ≈ 34 K both glass phases are independently verified by memory and rejuvenation effects. Biquadratic interaction of the Mn2+ spins with ferroelectric correlations of their off-center pseudospins in the incipient ferroelectric host crystal SrTiO3 explains the high spin glass temperature and comparably strong third-order magnetoelectric coupling between the polar and the magnetic degrees of freedom. Preliminary results on the related compound K0.97Mn0.03TaO3 favorably comply with the magnetoelectric multiglass concept.