We investigate a first-order extension of the Theory of Primitive Objects of [5] that supports method extension in presence of object subsumption. Extension is the ability of modifying the behavior of an object by adding new methods (and inheriting the existing ones). Object subsumption allows to use objects with a bigger interface in a context expecting another object with a smaller interface. This extended calculus has a sound type system which allows static detection of run-time errors such as message-not-understood, " width " subtyping and a typed equational theory on objects. Moreover, it can express classes and class-inheritance.