How to test classes that is derived from external base class which depends on external system

I have a class that is subclass of an external class over which I don't have any control. The external class depend on system resources. For example

class MyClass : public ExternalBase // This class is from external framework and framework requires it to derive from this class.
{
    int doSomePrivateThing(int );
public: 

    virtual int DoSomething(int );
    virtual ~MyClass();
}

int MyClass::doSomePrivateThing(int )
{
    // do some private task
}

int MyClass::DoSomething(int n)
{
    // Do MyClass Specific task
    int k = doSomePrivateThing(n);
    return ExternalBase::DoSomething(k); // This function depends on external system resources.
                                         // Probably try to communicate with remote server 
                                         // or attempt access Storage or Display device etc.
}

MyClass::~MyClass()
{}

How can I break the dependency of MyClass and write unit test for MyClass::DoSomething(). Using composition in place of inheritance is not a choice as framework requires classes to be derived from this base class.

I am using C++ and GoogleTest/Mock. But any generalized solution is appreciated.

Thanks in advance.