The purpose of this clinical trial is to learn if allogeneic cord blood-derived CAR-T cell drug works to treat Multiple Myeloma (MM) including Bone-related extramedullary (EMB) disease and extramedullary extraosseous disease(EME) in adults. It will also learn about the safety of the allogeneic cord blood-derived CAR-T cell drug. The main questions it aims to answer are:

1. What adverse events occur and the incidence rate of DLTs within 28 days and UCAR-T-related AEs within 28 days after the allogeneic cord blood-derived CAR-T cell injection for multiple myeloma (MM)?
2. Which dose level is the optimal biological dose (OBD)?
3. What is the overall responserate (ORR), including stringent complete response (sCR), completeresponse (CR),very good partial response (VGPR), partial response (PR), minimal Response (MR) and DOR, PFS, RFS, OS?

Participants will:

1. be pretreated with FC regimen, fludarabine (30mg/m²/d, days -5, -4, and -3) and cyclophosphamide (300~500 mg/m²/d, day -5,-4, and -3).
2. rest for 2 days on Day-2 and Day-1. Tumor burden should be re-evaluated and chemotherapy side effects assessment.
3. receive allogeneic cord blood-derived CAR-T cells infusion
4. Visit the clinic at D28, 1 month, 2 months, 3 months, 4 months, 6 months, 9 months and 1 year after CAR-T cells infusion.

Inclusion Criteria:

• 1.Aged 18 to 75 years (inclusive of boundary values), with no limitation on gender;

• 2.Diagnosed with multiple myeloma in accordance with the "Guidelines for the Diagnosis and Treatment of Multiple Myeloma in China (2022 Revision)" :

  1. Bone marrow monoclonal plasma cell percentage ≥10% and/or histopathological evidence of plasmacytoma; and presence of at least one of the following SLiM CRAB features:

     SLiM refers to:

     • S: Bone marrow monoclonal plasma cell percentage ≥60%;
     • Li: Ratio of involved to uninvolved serum free light chain ≥100 (with the involved light chain value being at least ≥100 mg/L);
     • M: MRI detection of >1 focal bone lesion larger than 5 mm.

     CRAB refers to:

     • C: Corrected serum calcium >2.75 mmol/L [Corrected serum calcium (mmol/L) = serum total calcium (mmol/L) - 0.025×serum albumin concentration (g/L) + 1.0 (mmol/L), or corrected serum calcium (mg/dl) = serum total calcium (mg/dl) - serum albumin concentration (g/L) + 4.0 (mg/dl)];
     • R: Renal insufficiency (creatinine clearance <40 ml/min or serum creatinine >177 μmol/L);
     • A: Anemia (hemoglobin < lower limit of normal by 20 g/L or <100 g/L);
     • B: Lytic bone lesions, demonstrated by radiographic imaging (X-ray, CT, MRI, or PET-CT) showing one or more lytic bone lesions.

  2. Definition of relapsed/refractory multiple myeloma:

     • Must have received at least three therapeutic regimens (The induction and maintenance therapies associated with hematopoietic stem cell transplantation, whether one or both were performed, are considered as one therapeutic regimen);
     • Must have been treated with a proteasome inhibitor, an immunomodulatory agent, or an anti-CD38 antibody;
     • Must be refractory to the last therapeutic regimen [refractory is defined as disease progression documented during or within 60 days after completion of the last anti-multiple myeloma therapeutic regimen (based on the last dose of the drug)].

• 3.Presence of at least one measurable lesion, meeting at least one of the following criteria:

  • Serum M protein ≥0.5 g/dL;
  • Urine M protein ≥200 mg/24 hours;
  • Serum free light chain (FLC) assay: involved FLC level ≥10 mg/dL (100 mg/L), provided that the serum FLC ratio is abnormal;
  • Biopsy-proven evaluable plasmacytoma;
  • Bone marrow plasma cells constituting >30% of total bone marrow cells;

• 4.Negative for Donor Specific Antibody (DSA);

• 5.The most recent assessment during the screening period indicates sufficient organ function, including renal and hepatic function, defined as:

  • Creatinine clearance rate ≥60 mL/min (calculated according to the Cockcroft-Gault formula);
  • Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤3×ULN (upper limit of normal);
  • Total bilirubin ≤1.5×ULN (for participants with a history of Gilbert's syndrome, total bilirubin ≤2.5×ULN).

• 6.Women of childbearing potential must have a negative serum pregnancy test within 7 days before enrollment. In this study, women of childbearing potential, their male partners with reproductive potential, and their partners must use effective contraception from the screening period until 12 months after UC503 administration. Women who are not of childbearing potential are defined as those who are at least 1 year postmenopausal or have documented infertility (congenital or acquired);

• 7.Written informed consent obtained before the initiation of any study-specific procedures.

Exclusion Criteria:

• 1.Participants meeting any of the following criteria are not eligible for enrollment in this study:
• 2.Lactating women;
• 3.Unwillingness to undergo follow-up for 15 years;
• 4.Poor compliance with the study procedures;
• 5.Individuals under legal guardianship or conservatorship;
• 6.with a history of ≥Grade 4 CRS or neurotoxicity in previous CAR-T therapy ;
• 7.Within 5 half-lives of prior anti-MM therapies (including approved therapies and other investigational drugs) before enrollment;
• 8.Disease progression after debulking therapy;
• 9.Active central nervous system (CNS) abnormalities or history of irreversible severe CNS toxicity from prior MM treatment leading to CNS organic lesions or CNS dysfunction;
• 10.Radioimmunotherapy or radiotherapy within 8 weeks before enrollment;
• 11.Hematopoietic stem cell transplantation (HSCT) within 3 months before screening, donor lymphocyte infusion within 6 weeks before screening; patients who have undergone autologous stem cell transplantation within 100 days; patients who have undergone solid organ transplantation;
• 12.Active acute or chronic graft-versus-host disease (GvHD) requiring systemic therapy within 4 weeks before UC503 cells infusion;
• 13.Patients with autoimmune diseases who are unable to discontinue systemic immunosuppressive therapy;
• 14.Patients currently receiving or having received high-dose (total dose of 60 mg dexamethasone or equivalent other corticosteroid) systemic corticosteroid therapy within 4 weeks before lymphodepletion;
• 15.Known hypersensitivity to UCAR-T or any of its components;
• 16.Any known uncontrolled cardiovascular disease within 6 months before enrollment, or any of the following conditions: ≥Grade 2 ventricular or atrial arrhythmias, ≥Grade 2 bradycardia, myocardial infarction, severe/unstable angina, symptomatic congestive heart failure, cerebrovascular accident or transient ischemic attack, pulmonary embolism, deep vein thrombosis, poorly controlled hypertension with standard medications. Or left ventricular ejection fraction (LVEF) < 45% as assessed by echocardiogram or multigated acquisition scan (MUGA) at screening;
• 17.Any known uncontrolled pulmonary disease within 6 months before enrollment, or any of the following conditions: pulmonary embolism, chronic obstructive pulmonary disease, history of idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis obliterans), drug-induced pneumonia, idiopathic pneumonia, or evidence of active pneumonia on chest CT scan at screening. A history of radiation pneumonitis/fibrosis within the radiation field is allowed, as well as symptomatic or poorly controlled interstitial lung disease, clinically significant pulmonary function abnormalities;
• 18.History of hypertensive crisis or hypertensive encephalopathy within 3 months before screening;
• 19.At enrollment, active bacterial, fungal, protozoal, or viral infections that are not effectively controlled despite adequate treatment, and positive blood cultures within 7 days before enrollment;
• 20.Undergone any major surgery within 3 months before screening;
• 21.Received any live-attenuated vaccine within 4 weeks before screening;
• 22.Any abnormal findings, medical conditions, or laboratory test results during the screening period that the investigator deems may jeopardize patient safety;
• 23.Any planned medical or surgical treatment that may interfere with the normal conduct of the study;
• 24.Presence of another malignancy within 2 years before screening (excluding in situ basal or squamous cervical cancer or cutaneous basal cell carcinoma);
• 25.Patient's psychiatric condition that prevents understanding of the nature, scope, and potential consequences of the study, and/or unwillingness to cooperate;
• 26.At enrollment, positive for hepatitis B surface antigen (HBsAg) or hepatitis B core antibody (HBcAb) with peripheral blood hepatitis B virus (HBV) DNA titer greater than the normal range; positive for hepatitis C virus (HCV) antibody with peripheral blood HCV RNA titer greater than the normal range; positive for human immunodeficiency virus (HIV) antibody; positive for human T-cell leukemia virus (HTLV) antibody; positive for Treponema pallidum antibody; positive for cytomegalovirus (CMV) DNA;
• 27.Contraindications to any drugs that may be used, including lymphodepleting agents such as fludarabine and cyclophosphamide, or agents maybe used for managing adverse events such as tocilizumab.

The IPD will be shared in a publication.

Beginning 3 months and ending 2 years after the publication of results