The language design process should be supported by modularity and abstraction in a manner that allows incremental changes as easily as possible. To at least partially fulfill this ambitious goal a new object-oriented attribute grammar specification language which supports multiple attribute grammar inheritance is introduced. Multiple attribute grammar inheritance is a structural organization of attribute grammars where the attribute grammar inherits the specifications from ancestor attribute grammars, may add new specifications or may override some specifications from ancestor specifications. With the proposed approach a language designer has the chance to design incrementally a language or reuse some fragments from other programming language specifications. The multiple attribute grammar inheritance is first introduced using an example, and thereafter by a formal model. The proposed approach is successfully implemented in the compiler/interpreter generator tool LISA ver. 2.0.