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Microflows constitute an important instrument to control particle dynamics. A prominent example is the sorting of biological cells, which relies on the ability of deformable cells to move transversely to flow lines. A classic result is that soft microparticles migrate in flows through straight microchannels to an attractor at their center. Here, we show that flows through wavy channels fundamentally change the overall picture. They lead to the emergence of a second, coexisting attractor for soft particles. Its emergence and off-center location depends on the boundary modulation and the particle properties. The related cross-stream migration of soft particles is explained by analytical considerations, Stokesian dynamics simulations in unbounded flows, and Lattice-Boltzmann simulations in bounded flows. The novel off-center attractor can be used, for instance, in diagnostics, for separating cells of different size and elasticity, which is often an indicator of their health status. [ABSTRACT FROM AUTHOR]