C++ Covariant Return Types for Multiple Hierarchies

Okay I've scrounged around the depths of SO and haven't been able to understand why this implementation of covariant return types is not working.

Say I have a return type hierarchy as follows:

class BaseData{
public:
    BaseData() = default;
    virtual ~BaseData() = 0;    //can't implement this
};
class DerivedData : public BaseData{
public:
    DerivedData() = default;
};
class DerivedData2 : public BaseData{
public:
    DerivedData2() = default;
};

and then I have some other hierarchy which would like to change which type of data is returned, depending on the class type. E.g.

class A {
public:
    A() = default;
    virtual ~A() = default;
    virtual BaseData* get_data() = 0;    //inheriting classes must implement this
};
class B : public A{
public:
    DerivedData* get_data();
};
class C public A {
public:
    DerivedData2* get_data();
};

Why do I get an "invalid covariant return types" error here since the derived data classes are instances of the base data class?

What design pattern is preferred here when I am trying to change the return-type depending on the sub-class, but would like to specify this function in the base through a pure virtual function?