Assuming many to many relation i.e.
An employee can work in multiple departments and a department has more than one employees
In that case each of the three tables(relations) mentioned will remain separate ; i.e. neither of them can be merged to other..In that case eid of "works" relation (which is a table of relationship between emp and dept entities) which is referencing to "employee" relation and did which references to "dept" relation..
Considering the case that a manager is also an employee so manager_id should be a valid eid..Hence manager_id should reference to eid..Hence manager_id can also be a foreign key under this scenario..
Hence number of foreign keys possible = 3 for the mentioned scenario..