There's not really a such thing as too many antibodies... They are a good thing. Too many white blood cells on the other hand is a sign of infection. Antibodies are the body's blueprints for fighting sickness. Well, technically allergies are a response to having too many antibodies, so there's that.
If you have too many antibodies in your system, you are likely to come down with a condition known as myeloma. This condition mainly affects the bone marrow and can be identified in blood. You cannot have too many antibodies, just enough.