• Male or female patients ≥ 18 years of age.

• Patients with sporadic or familial amyotrophic lateral sclerosis (ALS) diagnosed as laboratory-supported possible, probable, or definite according to World Federation of Neurology El Escorial Criteria.

• . Less than or equal to 24 months since ALS symptom onset.

• Total ALSFRS-R score between 34 and 45.

• Must have a source of autologous T cells potentially sufficient to manufacture RAPA-501 cells, as defined by a peripheral CD3+ T cell count ≥ 500 cells per μl.

• Patients may continue riluzole (Rilutek®), and/or edaravone (Radicava®), and/or sodium phenylbutyrate/taurusodial (Relyvrio™) if on a stable dose for at least 30 days prior to the screening visit.

• Patients must be ≥ 2 two weeks removed from major surgery or investigational therapy.

• Patients must have recovered from clinical toxicities (\[resolution of CTCAE(v5) \[version 5\] toxicity to a value of ≤ 2\].).

• Serum creatinine ≤ less than or equal to 2.0 mg/dL.

⁃ Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 3 x upper limit of normal (ULN).

⁃ Bilirubin ≤ 1.5 (except if due to Gilbert's disease).

⁃ Pulmonary slow vital capacity (SVC) ≥ 70% of predicted normal.

⁃ No history of abnormal bleeding tendency.

⁃ Voluntary written consent must be given before performance of any study related procedure not part of standard medical care, with the understanding that consent may be withdrawn by the patient participant at any time without prejudice to future medical care.