Yes. You can have separate UC diagrams focusing on different parts (functionalities) of your system and one of options is to split them by involved actors.
When you describe a system what you do is creating a model. A model is an abstraction of the actual thing (in this case of the system) intended to represent properties of the actual object. We're used to physical models, like scale model of a plane or car. There are also various reasons to build a model. You can build a model to show how something is going to look like or to test some physical properties (like aerodynamic drag).
Using an abstraction definition, a plan of a house, while might not be perceived as such, technically is also kind of house's model.
UML is intended to build models of systems (not only computer systems, however this is the main usage). To represent the system you need to model its various aspects and while the system is not a physical object the model has a form of diagrams depicting those aspects. A single diagram focus on a specific aspect of a system and to get the whole idea you need to study all of them. Thus all diagrams of the system combined constitute a model.
It's difficult if not impossible to show all aspects of even a simple system on a single diagram. Actually the number of diagram types comes from the fact that they focus on different aspects of the system, e.g. class diagram focuses on static data structures while activity diagram or state machine diagram focuses on changes of the system over time. It creates natural layer of abstractions and aspect borders.
But it is not the only limitation of modelling. To make it efficient model has to be understandable. with increasing complexity of the system it becomes impossible to depict all the information of one kind (e.g. data model or system functionalities) on just one diagram so to keep things clear those can be further split into smaller diagrams, adding new aspects. For classes it can focus on main business areas. For functionalities one of good options is separating the diagram by actors involved.
If you read into details of UML specification it clearly states, that the information on a single diagram is hardly ever complete information for the whole system. Even a full model might not cover all details.
So feel free to organise your diagram in a way that is most efficient to use for you and other stakeholders involved. And yes, of course you may produce multiple UC diagrams for a single system as long as they are consistent.
If you look at the UML specification, the class diagrams there represent the whole UML language model. Of course they are split into multiple class diagrams as otherwise they would be totally unreadable.
If you take any CASE system (like Enterprise Architect, Visual Paradigm, Rational Rose or even StarUML) you will find a difference between model and diagrams. Elements that you put on your diagram become parts of your model (usually visible in a form of a model tree) but it's not enough to remove element from a diagram to remove it from the model. Moreover if you drag two related elements from a model on a new diagram, they will automatically show with the relationship already presented.