This article describes the design of a common syntactic description for the core grammar of a group of related dialects. The common description does not rely on an abstract sub-linguistic structure like a metagrammar: it consists in a single FS-LTAG where the actual specific language is included as one of the attributes in the set of attribute types defined for the features. When the lang attribute is instantiated, the selected subset of the grammar is equivalent to the grammar of one dialect. When it is not, we have a model of a hybrid multidialectal linguistic system. This principle is used for a group of creole languages of the West-Atlantic area, namely the French-based Creoles of Haiti, Guadeloupe, Martinique and French Guiana.