The nonlinear signal mixing of two driving forces is used to control transport in overdamped ratchet devices. The interplay between the relative phase and the frequency ratio of the two driving forces is sufficient to generate an intriguing transport action that can be put to work to optimize shuttling and separation of particles in a variety of physical and technological applications. Analytic results for a striking multiple current reversal behavior including prominent, spikelike current features are obtained for doubly rocked and rocked-pulsated Brownian ratchets. This tunable signal mixing is readily implementable and exhibits even richer behaviors than those realized by the hard-to-implement modifiable-ratchet profiles.