It depends largely on what you mean by 'grammar'. If you mean the system of language as a system, Chomskyan Universal Grammar (UG) has already done so. Also, Halidayan Functional Grammar offers generalizations about all languages.
In fact, the task of general linguistics is to develop general models that make comparison between structures in particular languages possible. Grammar needs to be understood as a general instance that maps onto data from all languages, so that such data serve further development of the general model. What the model looks like is of course a question of which theory we consider. – Dual grammars are useful for purposes of automated translation, and may feed into the bigger linguistic picture.
Government and Binding as espoused by Noam Chomsky and simplified for instruction by Diane Blakemore opens the possibility of mapping two language structures under one tree structure. It accommodates and explains the phenomena of code mixing or code switching. It helps me map the grammatical structure of EL (an opaque language) and Bahasa Malaysia (a transparent language). I hope that helps unless I miss the question.