How to provide a void* accessor for a templated type?

I have a custom container class that is templated:

template<typename T>
class MyContainer {
  T Get();
  void Put(T data);
};

I would like to pass a pointer to this container to a function that will access the container's data as generic data - i.e. char* or void*. Think serialization. This function is somewhat complicated so it would be nice to not specify it in the header due to the templates.

// Errors of course, no template argument
void DoSomething(MyContainer *container);

I'm ok with requiring users to provide a lambda or subclass or something that performs the conversion. But I can't seem to come up with a clean way of doing this.

I considered avoiding templates altogether by making MyContainer hold a container of some abstract MyData class that has a virtual void Serialize(void *dest) = 0; function. Users would subclass MyData to provide their types and serialization but that seems like it's getting pretty complicated. Also inefficient since it requires storing pointers to MyData to avoid object slicing and MyData is typically pretty small and the container will hold large amounts (a lot of pointer storage and dereferencing).