Design pattern, interfaces etc

[deja]

I'm getting more and more confused as I try to sort this out clearly in
my head.

I have
abstract Class1 (includes Add method)
abstract Class1Extra(derives from Class1 with some extra properties)

concrete Class2(derives from Class1)
abstract Class3(derives from Class1Extra) with some extra methods etc.
concrete Class4(derives from Class3)
concrete Class5(derives from Class3)

I want Class 4 to have a different Add method signature to Class 5 and
Class 2 but I still want everything else that Class1Extra provides it.
I want the add methods mutually exclusive and ideally I want them
defined in an interface.

So, for example Class1 implements Interface1 which defines
Add(List<myobject>).
I want Class5 to implement Interface2 which defines
Add(List<otherobject>) but to retain the rest of the implementation of
its base class. I want to keep the strongtyping in the signature so
that if you call Class5.Add you can only pass in a list of
otherobjects.

I'm sure there's a basic solution but I'm going round in circles a bit
at the moment

TIA
Phil