Intracellular molecular motor-driven transport is essential for such diverse processes as mitosis, neuronal function, and mitochondrial transport. Whereas there have been in vitro studies of how motors function at the single-molecule level, and in vivo studies of the structure of filamentary networks, studies of how the motors effectively use the networks for transportation have been lacking. We investigate how the combined system of myosin-V motors plus actin filaments is used to transport pigment granules in Xenopus melanophores. Experimentally, we characterize both the actin filament network, and how this transport is altered in response to external signals. We then develop a theoretical formalism to explain these changes. We show that cells regulate transport by controlling how often granules switch from one filament to another, rather than by altering individual motor activity at the single-molecule level, or by relying on structural changes in the network.