Inclusion Criteria:  Subject and/or legal guardian must be able to understand the study procedures, have agreed to participate in the study and have voluntarily signed an IEC/IRB approved written informed consent. The consent form or a specific assent form, where required, will be signed and dated by minors. Have confirmed and documented clinical diagnosis of primary immunodeficiency disease including but not limited to: common variable immunodeficiency, X-linked and autosomal forms of agammaglobulinemia, hyper-IgM syndrome, or antibody deficiencies. Be male or female, and ≥ 2 years and < 12 years at the time of informed consent by subject or legal guardian. Have been receiving IGIV at a dose that has not been changed by > 25% of the mean dose on a mg/kg basis for at least 3 months prior to study entry. Have two trough levels of IgG in the last year (screening level may be used), and maintained a trough serum IgG level > 500 mg/dL on the previous 2 assessments prior to receiving Asceniv™. (The trough level must be at least 300 mg/dL above pre-treatment serum IgG levels; with exception for cases of X-linked agammaglobulinemia where no pre-treatment value is available. Documentation will need to include dose, treatment interval and trade name of the IGIV products used for the three doses prior to the first Asceniv™ infusion in this study. For female subjects, be of non-childbearing potential or have a negative pregnancy test prior to study start and be deemed not at risk of becoming pregnant by adherence to a reliable contraceptive method for the duration of the study. Females of non-childbearing potential are defined as prepubertal girls.  Exclusion Criteria:  Have a known hypersensitivity to immunoglobulin or any excipient in Asceniv™. Have a history of any severe anaphylactic or anaphylactoid reaction to blood or any blood-derived product. Have a specific Immunoglobulin A (IgA) deficiency (IgA ≤ 5 mg/dL and normal IgG and IgM), history of allergic reaction to products containing IgA or has demonstrable antibodies to IgA. Have uncompensated, hemodynamically significant, congenital or other heart disease. Including but not limited to acute coronary syndromes and chronic stable angina. Have a medical condition that is known to cause secondary immune deficiency, such as chronic lymphocytic leukemia, lymphoma, multiple myeloma, or HIV infection. Have a significant T-cell or granulocyte deficiency in number or function (chronic or recurrent absolute neutrophil count <1000 x 109/L). Have significant renal impairment (defined as an estimated Glomerular Filtration Rate ≤ 50 mL/min/1.73m2); or have a history of acute renal failure. Have abnormal liver function, defined as ALT or AST ≥ 2.5 x ULN. Have any chronic lung disease (uncontrolled or chronic, severe asthma, etc.) Have an infusion port, catheter, or other foreign body present (excluding PE tubes). Long-standing, infection-free ports may be permitted at the discretion of the Medical Monitor. Be planned or scheduled to undergo surgery during the course of study participation. Have ongoing failure to thrive per PI assessment. Be receiving chronic anti-coagulation therapy. Have a history of DVT, thrombotic or thrombo-embolic event, or are at increased risk for thrombotic event due to presence of, but not limited to, atrial fibrillation, disease or injury requiring prolonged immobilization, or other risk factor(s) including significant proteinuria or protein losing enteropathy.  Current daily use of the following medications:  corticosteroids (> 0.15 mg/kg/day of prednisone equivalent) Note: Intermittent corticosteroid use during the study is allowable, if medically necessary and approved by the ADMA Medical Director: i.e. 1 mg/kg twice a day for ten days to a maximum of 40 mg per dose immunomodulatory drugs (e.g. TNF (inhibitors -Enbrel, Humira, etc.) Xolair and Dupixent administration permitted. immunosuppressive drugs (excluding topical pimecrolimus (Elidel) and tacrolimus (Protopic)) Administration of a hyperimmune or specialty high titer Immunoglobulin product (e.g. Cytogam, VZIG, HBIG, etc.) within 30 days of screening, or expectation that a hyperimmune Immunoglobulin product will be given during the course of the study. Have uncontrollable arterial hypertension. Have anemia at screening (hemoglobin <10 g/dL). Have a history of hemolysis while undergoing treatment with IGIV therapy. Be morbidly obese as indicated by a Body Mass Index (BMI) ≥40. Have an active viral or bacterial infection or symptoms/signs consistent with such an infection, within the two weeks prior to the Screening Visit. Subjects may be receiving antibiotics as long as signs/symptoms of infection have been absent for two weeks prior to the initial infusion of investigational product (IP). Have received any blood product (other than Immunoglobulin G) within 3 months prior to screening. Have received any RSV specific products, including palivizumab (Synagis®) within 3 months prior to screening. Have abused alcohol, opiates, psychotropic agents, or other chemicals or drugs within the past 12 months. Have an acute or chronic medical condition that, in the opinion of the investigator, may interfere with the conduct of the study. Have any condition judged by the study physician to preclude participation in the study, including any psychological disorder, which might hinder compliance. Have any laboratory assessment result that, in the opinion of the investigator, warrants exclusion from participation in the study. Are currently pregnant or nursing. Have acute hepatitis A, acute or chronic Hepatitis B or C, or HIV infection. Have received investigational product within 3 weeks of the anticipated first infusion of Asceniv™.