Qualitative features of multiparticle correlations in light-heavy ion (p+A) collisions at RHIC and LHC are reproduced in a simple initial state model of partons in the projectile coherently scattering off localized domains of color charge in the heavy nuclear target. These include (i) the ordering of the magnitudes of the azimuthal angle nth Fourier harmonics of two-particle correlations v_{n}{2}, (ii) the energy and transverse momentum dependence of the four-particle Fourier harmonic v_{2}{4}, and (iii) the energy dependence of four-particle symmetric cumulants measuring correlations between different Fourier harmonics. Similar patterns are seen in an Abelian version of the model, where we observe v_{2}{2}>v_{2}{4}≈v_{2}{6}≈v_{2}{8} of two, four, six, and eight particle correlations. While such patterns are often interpreted as signatures of collectivity arising from hydrodynamic flow, our results provide an alternative description of the multiparticle correlations seen in p+A collisions.