I'm working on a component diagram of a system and due to the system's design quite a few dependency lines end up crossing, which makes the diagram hard to read and hard to follow.
One way to side-step this issue would be to use separate component diagrams to illustrate how a subset of the system's components depend on some component/interface. For example, the dependency on a data store would be represented in a component diagram which covers only the data stores and the components which directly access those datastores, omitting the remaining components. However, I'm not sure this is considered standard practice or even acceptable.
Does anyone know if it's ok to present multiple component diagrams of the same system? If not, what other alternatives are available to avoid cluttering the diagram?
Yes, that is the standard practice. Only the most trivial systems are small enough to be represented in a single diagram.