We study preheating in the Palatini formalism with a quadratic inflaton potential and an added αR 2 term. In such models, the oscillating inflaton field repeatedly returns to the plateau of the Einstein frame potential, on which the tachyonic instability fragments the inflaton condensate within less than an e-fold. We find that tachyonic preheating takes place when α ⪆ 1013 and that the energy density of the fragmented field grows with the rate Γ/H ≈ 0.011 α0.31. The model extends the family of plateau models with similar preheating behaviour. Although it contains non-canonical quartic kinetic terms in the Einstein frame, we show that, in the first approximation, these can be neglected during both preheating and inflation.