Weak entity primary key question

Hi all,
Say I have a weak entity whose primary key is a composite key made up of the primary keys of two strong entities (hence they are foreign keys). Is it possible then to have another weak entity related to that first weak entity, using those foreign keys as a composite key again in the new entity? Or should I simply make the first weak entity a strong one by giving it its own surrogate key, making the foreign keys simply normal keys in the table (no longer the entity's primary key), and use the new surrogate key as the primary key of the second weak entity? This is confusing I know, but I hope somebody can make sense of it. Thanks in advance.