Safety and Efficacy Study of Subcutaneous Belimumab and Intravenous Rituximab Co-administration in Subjects With Primary Sjogren's Syndrome

Inclusion Criteria: * Age \>=18 years, at the time of signing the informed consent. * Documented Primary Sjögren's Syndrome by American European Consensus Group criteria including: either anti-Sjogren's-syndrome-related antigen A (SS-A) or anti-Sjogren's-syndrome-related antigen B (SS-B) positive. * Baseline unstimulated salivary flow \>0.0 mL/min or evidence of glandular reserve function (stimulated baseline salivary flow \>0.05 mL/min). * Symptomatic oral dryness (\>=5/10 on subject completed numeric response scale). * Systemically active disease, ESSDAI \>=5 points. * Male and female subjects; females of child bearing potential are eligible if using effective contraception: Female subject is eligible to participate if she is not pregnant (as confirmed by a negative urine human chorionic gonadotropin \[hCG\] test), not lactating, and at least one of the following conditions applies: 1. Non-reproductive potential defined as: Pre-menopausal females with one of the following: Documented tubal ligation, Documented hysteroscopic tubal occlusion procedure with follow-up confirmation of bilateral tubal occlusion, Hysterectomy, Documented Bilateral Oophorectomy. Postmenopausal defined as 12 months of spontaneous amenorrhea (in questionable cases a blood sample with simultaneous follicle stimulating hormone \[FSH\] and estradiol levels consistent with menopause). Females on hormone replacement therapy (HRT) and whose menopausal status is in doubt will be required to use one of the highly effective contraception methods if they wish to continue their HRT during the study; otherwise, they must discontinue HRT to allow confirmation of post-menopausal status prior to study enrolment. 2. Reproductive potential and agrees to follow one of the options in the GlaxoSmithKline (GSK) Modified List of Highly Effective Methods for Avoiding Pregnancy in Females of Reproductive Potential (FRP) requirements from 30 days prior to the first dose of study medication up to Week 68 after Day 0. * Ability to understand and comply with the protocol-required procedures and provision of informed consent. Exclusion Criteria: * Diagnosis of secondary Sjögren's syndrome. * Active life-threatening or organ-threatening complications of Sjogren's-syndrome (SS) disease at the time of screening based on treating physician evaluation including but not restricted to (1) vasculitis with renal, digestive, cardiac, pulmonary or central nervous system (CNS) involvement characterized as severe, (2) active CNS or peripheral nervous system (PNS) involvement requiring high dose steroids, (3) severe renal involvement defined by objective measures, (4) lymphoma. * History of major organ transplant (including hematopoietic stem cell transplant). * History of malignancy within past 5 years (with the exception of adequately treated: \[1\] cervical carcinoma Stage 1B or less, \[2\] non-invasive basal cell and squamous cell skin carcinoma). * History of infection requiring long term systemic therapy including: (1) history of positive human immunodeficiency virus (HIV) serology, (2) positive serology for Hepatitis C virus (HCV), (3) positive serology for Hepatitis B (HB), defined as: HB surface antigen positive (HBsAg+) OR HB core antibody positive (HBcAb+). * Previous serious opportunistic or atypical infections or hospitalization for treatment of infection within 364 days of Day 0 or use of parenteral (intravenous \[IV\] or intramuscular \[IM\]) antibacterials, antivirals, anti-fungals, or anti-parasitic agents within 364 days of prior to Day 0. * Patients in a severely immunocompromised state. * History of an anaphylactic reaction to parenteral administration of contrast agents, human or murine proteins or monoclonal antibodies. * History of significant medical illness (or planned surgical procedure) which in the opinion of the investigator would interfere with the study procedures and / or assessments - including but not limited to immunoglobulin G4 (IgG4) disease or prior head or neck irradiation. * Severe heart failure (New York Heart Association, Class IV) or other severe, uncontrolled cardiac disease. * Tuberculosis (TB), defined as: prior history of TB infection; suspicion of TB infection or current TB infection * At risk of suicide, as indicated by a lifetime history of attempted suicide or significant suicidal ideation over the 6 months prior to the screening visit; or, if in the Investigator's judgment, the subject is at risk for a suicide attempt. * Neurological findings consistent with Progressive Multifocal Leukoencephalopathy (PML) - not otherwise explained - or confirmed PML. * Electrocardiogram (ECG) showing a clinically significant abnormality at Screening or showing an average corrected QT using Bazett's formula (QTcB) or corrected QT using Fridericia's formula (QTcF) interval \>=450 milliseconds (msec) (\>=480 msec for subjects with a Bundle Branch Block) over 3 consecutive ECGs. * Alanine aminotransferase (ALT) \>2x upper limit of normal (ULN) and bilirubin \>1.5xULN (isolated bilirubin \>1.5xULN is acceptable if bilirubin is fractionated and direct bilirubin \<35%). * Current or chronic history of liver disease, or known hepatic or biliary abnormalities (with the exception of Gilbert's syndrome or asymptomatic gallstones) * Use of systemic immunosuppressive or immunomodulatory agents including methotrexate, azathioprine, leflunomide, mycophenolate (including mycophenolate mofetil, mycophenolate mofetil hydrochloride, and mycophenolate sodium), mizoribine, calcineurin inhibitors \[e.g., tacrolimus, cyclosporine\], sirolimus, 6-mercaptopurine, or thalidomide within 60 days prior to Day 0. * Have received cyclophosphamide within 180 days prior to Day 0. * Have received anti- B lymphocyte stimulator (BLyS), anti-CD 20, anti-CD22 or anti-CD52 or any other B-cell depleting agent within 364 days prior to Day 0. * Have received abatacept or any biologic agent within 180 day prior to Day 0 (with exception of denosumab). * Have received intravenous immunoglobulin (IVIG) or plasmapheresis within 90 days prior to Day 0. * Have received oral steroid \>10 milligram (mg) prednisone equivalent/day within 30 days prior to Day 0 or oral steroid \>20 mg prednisone equivalent / day for a minimum of two consecutive weeks within 60 days prior to Day 0. Have received parenteral steroid within 60 days prior to Day 0. * Have received a live vaccine within 30 days of Day 0. * Current participation in any other interventional trial. * Planned blood donation during the treatment and follow up periods of the study. * Subjects who are unable or unwilling to administer, or to have a caregiver administer subcutaneous injections. * Drug or alcohol abuse or dependence. * History of hypersensitivity to belimumab and/or rituximab or known to have titers of human anti-mouse antibody or human anti-chimeric antibody or history of hypersensitivity reactions when treated with other diagnostic or therapeutic monoclonal antibodies. * Have an IgA deficiency (IgA level \<10 milligram per deciliter \[mg/dL\]). * Any of the following screening laboratory values: White blood cells (WBC) \<2 x 10\^9/L; Neutrophils \<1.5 x 10\^9/Liter (L); Circulating IgG or IgM levels \<lower limit of normal (according to central laboratory range); Aspartate aminotransferase (AST) \>2.0 times the upper limit of normal; Alkaline phosphatase (ALP) \>1.5 times the upper limit of normal; Bilirubin \>1.5 times the upper limit of normal; CD4 count \<400 cells per cubic millimetre (cells/mm\^3); CD8 count \<150 cells/mm\^3; CD19+ B-lymphocyte counts \<0.1 x 10\^9/L.