Sort of multiple inheritance?

I have the following class structure (Blah === ExtBlah):

Base
 +--[ ExtBase ]    --???-- [ ExtBlah ] --- .. more scripts ...
 +--[ Blah ]
        +---[ Script1 ]
        +---[ Script2 ]
        +---[ ....... ]
        +---[ ScriptN ]     

Now I need to write more Scripts which need to extend Blah, but Blah has to extend "ExtBase", instead of "Base" for the new script cases.

I still have to have Blah the way it is because the Scripts1-N have to be dependent on "Base", not on "ExtBase".

Also I don't want to create a copy of Blah i.e. ExtBlah, because that mean duplication of code and will be harder and messier to support.

Any ideas ?