A Study to Investigate the Safety and Preliminary Efficacy of ALLO-329, an Allogeneic CAR T-cell Therapy, in Adults With Autoimmune Disease

Inclusion Criteria: 1. Adults ≥ 18 to \< 75 years of age. 2. Adequate hematological function and liver, cardiac, and pulmonary function. 3. A highly sensitive urine pregnancy test or serum pregnancy test (for females of childbearing potential) negative at screening. All participants of childbearing potential must be willing to use a highly effective method of contraception for at least 12 months for females (6 months for males) after LD chemotherapy or ALLO-329 administration, whichever is later. 4. Signed and dated informed consent form. 5. Willing and able to comply with scheduled visits, treatment plan, laboratory tests, and other procedures. 6. Confirmed active disease (SLE, IIM, or SSc) as defined by the appropriate classification criteria for each respective disease, clinical evidence, and/or laboratory testing. 7. Disease activity as above despite prior treatment with standard of care therapy including at least one immunosuppressive agent for at least 3 months. Exclusion Criteria: 1. Participants with active systemic bacterial, fungal, or viral infection requiring systemic treatment or a clinically significant active, opportunistic, chronic or recurrent infection. 2. Any active malignancy within 5 years prior to enrollment, except for adequately treated localized basal cell or squamous cell skin cancer, carcinoma in situ or low risk prostate cancer (Gleason score ≤ 6) under observation. Prior treatment of cancer with curative intent which in the opinion of the treating oncologist has less than a 10% chance of recurrence in the next 10 years can be allowed after discussion with the sponsor. 3. Prior treatment with CD19 or CD70 targeted therapy or any prior engineered cell therapy (e.g., CAR T therapy), except prior treatment with ALLO-329 in this study. 4. Clinically significant or unstable or uncontrolled acute or chronic disease (e.g., hypothyroidism and diabetes). 5. Symptomatic cardiac or vascular disease requiring medical intervention within 6 months prior to screening, hemodynamically symptomatic pericardial effusion, or symptomatic electrocardiogram abnormality requiring medical intervention. 6. Child-Pugh Class B or C cirrhosis. 7. Symptomatic airway disease requiring medical intervention, pleural effusion ≥ Grade 2, or history of pulmonary embolism requiring anticoagulant therapy within 6 months of ALLO-329 dosing. 8. Participants known to be refractory to platelet or red blood cell transfusions or who will refuse indicated transfusion support to manage cell counts following treatment. 9. Any form of primary, inherited immunodeficiency. 10. Unwilling to participate in an extended safety monitoring period. 11. For participants with SLE: History or active disease involving CNS within the last 6 months or SLE that is drug-induced. For those with lupus nephritis, history of dialysis within 12 months prior to signing the informed consent form or expected need for renal replacement therapy within the next 12 months after dosing, or National Institutes of Health (NIH) chronicity score of 3+ in any of the following domains: glomerular sclerosis, glomerular fibrous crescents, tubular atrophy, and/or interstitial fibrosis. 12. Participants with IIM: A myositis other than specified classification per exclusion criteria, non-reversible, unrelated or weakness not amenable to assessment, or dermatomyositis with presence of anti-TIF1 gamma antibody. 13. Participants with SSc: Pulmonary arterial hypertension requiring treatment, rapidly progressive or severe SSc gastrointestinal involvement, or prior scleroderma renal crisis.