The main objective of this study is to see if GAMMAPLEX is efficacious with respect to Food and Drug Administration (FDA) minimal requirements (no more than 1 serious, acute, bacterial infection per subject per year) in subjects with Primary Immunodeficiency Diseases (PID). The secondary objectives are to assess the safety and tolerability of GAMMAPLEX and to determine if GAMMAPLEX has a pharmacokinetic (PK) profile comparable with that of intact Immunoglobulin G (IgG) in subjects with PID.