  We study preheating in the Palatini formalism with a quadratic inflaton
potential and an added $\alpha R^2$ 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
$\alpha \gtrsim 10^{13}$ and that the energy density of the fragmented field
grows with the rate $\Gamma/H \approx 0.011 \times \alpha^{0.31}$. 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.
