Associations with composit IDs when associated fields are not all part of the IDs

Got a rather unruly and unfortunate situation where I have two tables with composite IDs that have a many-to-many association where not all of the referencing fields belong to the IDs. Hard to explain, so here are example classes that

public class Class1
{

public string A; // part of the compositeID
public string B; // part of the compositeID
public string C; // not part of the compositeID, but is part of the association to Class2
public IList<Class2> Class2List;

}

public class Class2
{

// all compositeID keys
public string B;
public string C;
public string D;

}

public class Class1Map : ClassMap
{

public Class1Map()
{
    CompositeId()
        .KeyProperty(x => x.A)
        .KeyProperty(x => x.B);

    Map(x => x.C);

    // how do i map for Class2List?  
    // The following gives a NHibernate.FKUnmatchingColumnsException:
    HasManyToMany(x => x.Class2List)
        .ParentKeyColumns.Add("B")
        .ParentKeyColumns.Add("C");
}

}

public class Class2Map : ClassMap
{

public Class2Map()
{
    CompositeId()
        .KeyProperty(x => x.B)
        .KeyProperty(x => x.C)
        .KeyProperty(x => x.D);
}

}

Is this possible to map?