"I think, though am not at all sure, that pathogens need to invade cells to be dangerous."
True in the case of viruses and some bacteria.
Hiding within the cells of the host is the intracellular pathogenesis.
But other "tricks" are possible. Four examples:
surface proteins that "catch" antibodies
fast mutation of ...
Alright, there are two major questions:
(a) Are all the antibodies that are produced against a specific antigen necessarily identical?
Not in most cases. Antigens can either be monovalent or polyvalent, meaning that they can either have one epitope or various different epitopes (an epitope is the site of the antigen that binds to a T-cell receptor or a B-...