Autologous Stem Cell Transplant for Neurologic Autoimmune Diseases

Inclusion Criteria: * Patients with an autoimmune disorder of the central or peripheral nervous system will be eligible; this will include: * Primary Central Nervous System (CNS) vasculitis * Rasmussen's encephalitis * Autoimmune peripheral neuropathy (anti-Hu \[Anna-1\], anti-GM1 \[GD1b\], anti-MAG, anti-ganglioside, anti-sulfatide) * Autoimmune cerebellar degeneration * Gait Ataxia with Late age Onset Polyneuropathy (GALOP) * Stiff Person Syndrome * Chronic Inflammatory Demyelinating Polyneuropathy * Myasthenia Gravis * Lambert-Eaton myasthenic syndrome * Human T-cell lymphotropic virus (HTLV)-1-associated myelopathy (HAM) / tropical spastic paraparesis (TSP) * Opsoclonus/myoclonus (anti-Ri) * Neuromyelitis optica * Multiple sclerosis * Other central or peripheral nervous system autoimmune diseases as approved by study neurologists and the Fred Hutchinson Cancer Research Center (FHCRC) faculty at Patient Care Conference (PCC) * Patients must satisfy the criteria for a diagnosis of one of the severe neurological autoimmune disorders outlined * Patients age =\< 70 years * Evidence of disease activity as outlined (e.g. gadolinium enhancement on magnetic resonance imaging of the brain or clinical progression) * Patients must have failed at least 2 lines of standard therapy as outlined for the specific diseases * DONOR: Sibling of any patient enrolled on this protocol proven by ABO typing, human leukocyte antigen (HLA) typing and variable number tandem repeat (VNTR) analysis to be syngeneic with the patient (e.g. identical twin) * DONOR: Willing to undergo multiple apheresis procedures (except donors \< 12 years who will undergo bone marrow harvests) Exclusion Criteria: * Age \>= 71 years * Pregnancy or expressed plans to become pregnant within 1 year of the procedure * Patients who are serologically positive for human immunodeficiency virus (HIV) * Patients with pulmonary, cardiac, hepatic or renal impairment that would limit their ability to receive cytoreductive therapy and compromise their survival; this should include patients with any of the following: * Severe pulmonary dysfunction associated with a carbon monoxide diffusing capacity (DLCO) (corrected for hemoglobin) \< 60%, or requires supplemental oxygen; patients who are unable to perform pulmonary function test (because of underlying disease) will be excluded if the oxygen saturation is \< 92% on room air * Uncontrolled malignant arrhythmias, or clinical evidence of congestive heart failure (New York class III-IV) or ejection fraction \< 50% * Renal disease with estimated glomerular filtration rate (GFR) by creatinine clearance or iothalamate clearance \< 50 ml/min/1.73 m\^2 body surface area * Serum glutamate pyruvate transaminase (SGPT)/aspartate aminotransferase (AST) \> 3 times normal or direct bilirubin greater than 2.5 mg/dL on two repeated tests * Active uncontrolled infection * Demonstrated lack of compliance with prior medical care * Patients whose life expectancy is limited by illness other than their neurological condition * Patients with evidence of myelodysplasia * Active malignancy (excluding localized squamous cell or basal cell carcinoma of the skin) * DONOR: Inadequate documentation that donor and recipient are syngeneic * DONOR: Donors who do not fulfill criteria as apheresis donors as established by institutional guidelines * DONOR: Concordant for autoimmune neurological disease(s) as determined by neurological evaluation