We investigate extensions to the class of maximal Cohen-Macaulay modules over Cohen-Macaulay rings from the viewpoint of definable subcategories. We pay particular attention to two definable classes that arise naturally from the definition of the Cohen-Macaulay property. A comparison between these two definable subcategories is made, as well as a consideration of how well these classes reflect the properties of the maximal Cohen-Macaulay modules and relate to Hochster's balanced big Cohen-Macaulay modules. In doing so we explore homological and categorical properties of both classes. A more detailed consideration is given to the role cotilting plays in this discussion. We show both these definable classes are cotilting and completely describe their cotilting structure, including properties of their corresponding cotilting modules. This approach yields further information about the classes and their closure properties.