Extending a third party tagged type while adding finalization

[Jere <jhb.chat@gmail.com>]

Has anyone have any good tips for extending a third party type:

type Third_Party_Type is tagged private;

I want to extend it but also add finalization which is inheritable
by later descendants:

type My_Base_Type is new Third_Party_Type with private;
procedure Finalize(Object : in out My_Type);
procedure Initialize(Object : in out My_Type);
procedure Adjust(Object : in out My_Type);

That way, clients of My_Base_Type can use them along side Third_Party_Type such
as through a variable of Third_Party_Type'Class.  My first (untested) thought
is to maybe string together a proxy object inside My_Base_Type using the
Rosen technique and have it forward the Finalization operations through 
dispatch.  I haven't tested this to see if it works but even if it does, it
feels very hacky and is not my preferred way.

Does anyone have any techniques they have used in the past?