1. Confirmed diagnosis of MS according to the 2017 McDonald criteria . 2. Age 18 years to age 75 years. 3. Confirmed clinical diagnosis of non-active SPMS, for 2 years prior to the screening visit. The baseline study visit and/or the baseline MRI may not be used to confirm the diagnosis but will be used to establish a study baseline and for interpretation of the PET scan data. The second qualifying MRI must be within 3 months of the study screening MRI. 4. MRI imaging consistent with a diagnosis of MS at any time point. 5. Score on the Expanded Disability Status Scale (EDSS) of 2.5-6.5. 6. Have failed standard-of-care treatment with disease-modifying therapies for at least 2 years with continued accumulation of disability as evaluated by treating neurologist. Treatment failure/progression can be defined as EDSS worsening despite best treatment efforts:

• - EDSS increase by 1.0 (if baseline EDSS between 1.0-5.5) in the past 2 years.

• - EDSS increase by 0.5 (if baseline EDSS >6.0) in the past 2 years.

7. Screening clinical laboratory studies are within the normal ranges or within the parameters specified below, and clinically acceptable in the opinion of the Investigator. Exceptions must be approved by the CRO or Sponsor's Medical Monitor.

• - Adequate hematologic parameters without ongoing transfusion support: - Hemoglobin (Hb) ≥9 g/dL.

• - Platelets ≥100 × 10^9 cells/L.

• - Creatinine ≤1.5 × the upper limit of normal (ULN), or calculated creatinine clearance ≥60 mL/minute × 1.73 m^2 per the Cockcroft-Gault formula.

• - Total bilirubin ≤1.5 times the upper limit of normal (ULN) unless due to Gilbert's disease.

• - Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤2.0 times ULN.

8. Negative serum pregnancy test at screening and negative urine pregnancy test within 7 days prior to the first dose of study therapy for women of child-bearing potential, defined as a sexually mature woman who has not undergone a hysterectomy or who has not been naturally postmenopausal for at least 24 consecutive months (i.e., who has had menses any time in the preceding 24 consecutive months). 9. Sexually active women of child-bearing potential and male patients must agree to use 2 effective methods to avoid pregnancy (oral, injectable, or implantable hormonal contraceptives; tubal ligation; intra-uterine device; barrier contraceptive with spermicide; or vasectomized partner) throughout the study, and for 90 days after the completion of study treatment. 10. Immunizations are current and up-to-date as adjusted for disease status and prior/current treatments, and documented by the patient's treating neurologist. 11. Ability and willingness to provide written informed consent.

Exclusion Criteria:

1. Corticosteroid use (oral or intravenous) within the last 60 days or anticipated need for such treatment during the study period. 2. Current use or use within 30 days prior to the screening visit of interferon, glatiramer acetate, fingolimod, siponimod, dimethyl fumarate, ponesimod, ozanimod, cyclosporin, methotrexate, azathioprine, mycophenolate mofetil, natalizumab or any other chronic immunosuppressive medication. Concomitant immunomodulatory or immunosuppressant treatments for MS are not permitted during study participation. 3. Patient in whom the need to start or stop other pharmacologic treatment for MS is expected during the time of the study or the need for initiation of B cell depleting therapies (e.g. ocrelizumab, ofatumumab, rituximab) during the study. 4. Use of B cell depleting therapies (e.g. ocrelizumab, ofatumumab, rituximab) within the prior 6 months. Or use of terifluonimide within the previous 6 months. 5. Patients with any previous exposure to alemtuzumab, cyclophosphamide, cladribine, mitoxantrone, or daclizumab. 6. Prior use of AHSCT or stem cell therapy. 7. Inability to tolerate nasally administered medications. 8. Nasal corticosteroids, nasal antihistamines, nasal flu dosing within the past 60 days. 9. Active COVID-19 disease; according to FDA guidelines. 10. Female patient who is pregnant, lactating, breastfeeding, or planning on becoming pregnant during the study. Female patients of childbearing age will undergo a serum pregnancy test at screening and be excluded from the study if positive. Urine pregnancy testing will be carried out prior to each dosing cycle, and the patient's study participation will be stopped if there is a positive result. Pregnancy testing will also be performed prior to each MRI or PET imaging session and participation in the imaging session and the study will be terminated if positive. 11. Any history of malignancy or active malignancy. 12. Inflammatory bowel disease, rheumatoid arthritis, systemic lupus erythematosus, asthma, or type 1 diabetes. 13. Patients with a history of gadolinium allergy or any other contraindications to MRI, such as metal implants, chronic renal disease, and an eGRF of <30 mL/minute or claustrophobia, or who are unable to lay flat in the PET or MRI scanner for the duration of the studies. 14. A low affinity translocator protein (TSPO) binder (for PET ligand [18F]PBR06) determined by having a Thr/Thr polymorphism in the TSPO gene at screening. 15. EBV IgM-positive patients, assessed at screening. Patients will also be excluded if they have a documented history of being EBV positive, even if the testing at screening is negative. 16. Known positivity for human immunodeficiency virus (HIV), hepatitis B virus surface antigen (HBsAg), or hepatitis C virus (HCV) or tuberculosis at screening. If the patient has a history of positivity for any of these diseases, they are excluded even if current screening is negative. 17. Patients with a neutrophil count at baseline of <1000 cells/mL or lymphocytes <500 cells/mL. 18. Any nasal pathology such as clinically significant deviated septum, nasal polyps, chronic rhinitis, or a history of sinusitis diagnosed or treated in the past 12 months. 19. Clinically significant cardiac condition or ECG abnormality at screening or by history. An ECG will be done prior to each dosing cycle and patients will be excluded or treatment discontinued for any significant ECG abnormality. 20. Any other medical intervention or other condition which, in the opinion of the Principal Investigator, could compromise adherence to study requirements or confound the interpretation of study results. 21. A history of recent infections or treatment for infections. 22. Receipt of an investigational drug/biological product in the past 30 days of screening, or concurrent receipt of an investigational during this study, other than the product under study. Patients may not have previously received treatment with foralumab nasal.

Multiple sclerosis (MS) is a common autoimmune disorder affecting young adults, driven by an aberrant T cell response against central nervous system (CNS) antigens. Epidemiologic studies show that approximately 50% of patients are classified as having relapsing-remitting multiple sclerosis (RRMS), while about 35% have SPMS and the remaining 15% have primary progressive MS (PPMS). Foralumab is a human anti-CD3 monoclonal antibody being developed for the treatment of autoimmune and inflammatory diseases. It is hypothsized that nasal foralumab will slow disability accumulation and microglial activation measured by PET imaging in non-active SPMS. This study is a randomized, double-blind, placebo-controlled, multicenter, parallel-group study of 2 doses of nasal foralumab (50 μg/dose or 100 μg/dose of foralumab nasal) compared to placebo in the treatment of non-active SPMS for 3 months (4 three-week cycles of treatment). Fifty-four subjects with non-active SPMS will be randomized 1:1:1 to one of three treatment cohorts: 1. Group A: Nasal foralumab 50 μg 3 days a week (Monday-Wednesday-Friday) for two weeks, followed by a one-week rest, comprising a 3-week cycle, for a total of four cycles. 2. Group B: Nasal foralumab 100 μg 3 days a week (Monday-Wednesday-Friday) for two weeks, followed by a one-week rest, comprising a 3-week cycle, for a total of four cycles. 3. Group C: Nasal placebo (acetate buffer) 3 days a week (Monday-Wednesday-Friday) for two weeks, followed by a one-week rest, comprising a 3-week cycle, for a total of four cycles.

Arms

Experimental: Nasal Foralumab 50 μg

Each patient will receive nasal foralumab 50 μg per dosing day (25 μg per nostril).

Experimental: Nasal Foralumab 100 μg

Each patient will receive nasal foralumab 100 μg per dosing day (50 μg per nostril).

Placebo Comparator: Nasal placebo (acetate buffer)

Each patient will receive placebo on each dosing day in divided doses, in each nostril.

Interventions

Drug: - Foralumab

Foralumab nasal solution is a preservative-free, sterile, clear, colorless-to-slightly-yellow solution filled in an Aptar Unidose nasal atomizer device. Each Unidose device contains 0.13 mL foralumab placebo nasal solution, sufficient for administration to a single nare. Two Aptar Unidose devices will be used for a single dose (one device per nare). Each Unidose device contains foralumab nasal solution, supplied at either 25 μg foralumab or 50 μg foralumab, sufficient for administration into a single nare.

Other: - Placebo

Foralumab placebo nasal solution is a preservative-free, sterile, clear, colorless-to-slightly-yellow solution filled in an Aptar Unidose nasal atomizer device. Each Unidose device contains 0.13 mL foralumab placebo nasal solution, sufficient for administration to a single nare. Two Aptar Unidose devices will be used for a single dose (one device per nare).