Evaluating Alemtuzumab as a Treatment in Stabilizing Neurocognitive Function In Relapsing Remitting Multiple Sclerosis Patients

Inclusion Criteria: 1. Signed informed consent form (ICF) 2. Age 18 to 55 years old (inclusive) as of the date the ICF is signed 3. Diagnosis of MS per McDonald criteria (2005 update). 4. Onset of MS symptoms (as determined by a neurologist, at present or retrospectively) within 10 years of the date the ICF is signed 5. EDSS score 0.0 to 5.0 (inclusive) at Screening 6. ≥ 2 MS attacks (first episode or relapse) occurring in the 24 months prior to the date the ICF is signed, with ≥ 1 attack in the 12 months prior to the date the ICF is signed, with objective neurological signs confirmed by a physician, nurse practitioner, or other sponsor-approved health-care provider. The objective signs may be identified retrospectively. 7. ≥ 1 MS attack (relapse) during treatment with a beta interferon therapy or glatiramer acetate after having been on that therapy for ≥ 6 months within 10 years of the date the ICF is signed 8. MRI scan demonstrating white matter lesions attributable to MS and meeting at least 1 of the following criteria, as determined by the neurologist or a radiologist * ≥ 9 T2 lesions at least 3 mm in any axis * a gadolinium-enhancing lesion at least 3 mm in any axis plus \> 1 brain T2 lesions * a spinal cord lesion consistent with MS plus \> 1 brain T2 lesions 9. Corrected vision of subjects must be no worse than 20/50. 10. Participants must have at least 10 years of education. 11. Participants must be capable of writing and pressing the buttons on a computer mouse. 12. Participants must be capable of understanding and following all test instructions. Exclusion Criteria: Patients will be excluded from enrollment in this study if they meet any of the following criteria: 1. Previous treatment with alemtuzumab 2. Current participation in another clinical study or previous participation in CAMMS323 3. Treatment with natalizumab, methotrexate, azathioprine, or cyclosporine in the past 6 months. Patients who received one of these medications more than 6 months before the date the ICF is signed may be eligible for study entry if approval is granted by the sponsor 4. Previous treatment with mitoxantrone, cyclophosphamide, cladribine, rituximab or any other immunosuppressant or cytotoxic therapy (other than steroids) 5. Previous treatment with any investigational medication (drug has not been approved at any dose or for any indication) unless prior approval is granted by the sponsor and the patient completes any required washout. Use of an investigational medication that was subsequently licensed and nonstandard use of a licensed medication (eg, using a dose other than the dose that is stated in the licensed product labeling or using a licensed therapy for an alternative indication) is not exclusionary. Prior treatment with herbal medications or nutritional supplements is also permitted. 6. Any progressive form of MS 7. History of malignancy, except basal skin cell carcinoma 8. Any disability acquired from trauma or another illness that, in the opinion of the Investigator, could interfere with evaluation of disability due to MS 9. Previous hypersensitivity reaction to any immunoglobulin product 10. Known allergy or intolerance to interferon beta, human albumin, or mannitol 11. Intolerance of pulsed corticosteroids, especially a history of steroid psychosis 12. Inability to self-administer SC injections or receive SC injections from caregiver 13. Inability to undergo MRI with gadolinium administration 14. Confirmed platelet count \< the lower limit of normal (LLN) of the evaluating laboratory at Screening or documented at \<100,000/μL within the past year on a sample without platelet clumping 15. Absolute neutrophil count \< LLN at Screening; if abnormal cell count returns to within normal limits, eligibility may be reassessed 16. Known bleeding disorder (eg, dysfibrinogenemia, factor IX deficiency, hemophilia, Von Willebrand's disease, disseminated intravascular coagulation \[DIC\], fibrinogen deficiency, clotting factor deficiency) 17. Seropositivity for human immunodeficiency virus (HIV) 18. Significant autoimmune disease including but not limited to: immune cytopenias, rheumatoid arthritis, systemic lupus erythematosus, other connective tissue disorders, vasculitis, inflammatory bowel disease, severe psoriasis. 19. Active infection, eg, deep-tissue infection, that the Investigator considers sufficiently serious to preclude study participation 20. In the Investigator's opinion, is at high risk for infection (eg, indwelling catheter, dysphagia with aspiration, decubitus ulcer, history of prior aspiration pneumonia or recurrent urinary tract infection) 21. Latent tuberculosis unless effective anti-tuberculosis therapy has been completed, or active tuberculosis. 22. Infection with hepatitis C virus 23. Past or present hepatitis B infection (positive hepatitis B serology) 24. Of childbearing potential with a positive serum pregnancy test, pregnant, or lactating 25. Unwilling to agree to use a reliable and acceptable contraceptive method throughout the study period (fertile patients only). Reliable and effective contraceptive method(s) include: intrauterine device (IUD), hormonal based contraception, surgical sterilization, abstinence, or double-barrier contraception (condom and occlusive cap (diaphragm or cervical cap with spermicide). 26. Major psychiatric disorder that is not adequately controlled by treatment 27. Epileptic seizures that are not adequately controlled by treatment 28. Major systemic disease or other illness that would, in the opinion of the Investigator, compromise patient safety or interfere with the interpretation of study results, e.g., current peptic ulcer disease, or other conditions that may predispose to hemorrhage 29. Medical, psychiatric, cognitive, or other conditions that, in the Investigator's opinion, compromise the patient's ability to understand the patient information, to give informed consent, to comply with the trial protocol, or to complete the study 30. Prior history of invasive fungal infections 31. Cervical high risk human papillomavirus (HPV) positivity or abnormal cervical cytology other than abnormal squamous cells of undetermined significance (ASCUS). The patient may be eligible after the condition has resolved (e.g., follow-up HPV test is negative or cervical abnormality has been effectively treated). 32. Any other illness or infection (latent or active) that, in the Investigator's opinion, could be exacerbated by either study medication 33. Any hepatic or renal function value grade 2 or higher at Screening, with the exception of hyperbilirubinemia due to Gilbert's syndrome, unless, in the Investigator's opinion, the abnormality is due to a condition that has resolved (eg, recent interferon treatment subsequently discontinued) and levels return to within normal limits. See Table below, drawn from the National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events v3.0 (CTCAE), published 09 August 2006. * Hepatic * Bilirubin \> 1.5 × ULN * SGOT/AST \> 2.5 × ULN * SGPT/ALT \> 2.5 × ULN * Alkaline phosphatase \> 2.5 × ULN * Renal * Creatinine \> 1.5 × ULN 34. Participants with upper extremity dysfunction which prohibits them from using a computer mouse. 35. Participants who are colorblind. 36. Participants with current alcohol/substance abuse. 37. Participants taking medications with notable adverse CNS effects such as excessive sedation.