If operations can be grouped by functional area, they must be separate services, because a service like any other class should have a single responsibility = a single functional area.
As a rule, if your service has many operations, the time has come to split it. In addition, more often than not, the WCF service is just a wrapper around some logic, so you can create instances of other classes that wrap your logic, or use static classes in your service operations.
Edit:
In general, I am opposed to using partial classes to break a large class - in my opinion, this does not improve maintainability. When the class is so large that you are looking for a solution to split it into multiple files, this already means that refactoring should have been done a long time ago. In the worst case scenario, when your class does too much, we can call it an anti-pattern: an object of God .
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