Inclusion Criteria:  Participant has provided informed consent prior to initiation of any study specific activities/procedures. Age 18 years or older at the time of signing the informed consent. Relapsed or relapsed and refractory multiple myeloma according to International Myeloma Working Group (IMWG) criteria. Participants must have received ≥ 3 prior therapies that must include all approved and available therapies deemed eligible by the investigator, including at a minimum, a proteasome inhibitor (PI), an immunomodulatory drug (IMiD), and a CD38-directed antibody. Note: Participants may have received prior treatment targeting BCMA that is not AMG 701.  Participants must have measurable disease, defined by 1 or more of the following at time of screening :  A serum M protein ≥ 0.5 g/dL measured by serum protein electrophoresis (SPEP) Urinary M protein excretion ≥ 200 mg/24 hours Involved serum free light chain (sFLC) measurement ≥ 10 mg/dL, provided that SFLC ratio is abnormal as per IMWG response criteria Eastern Cooperative Oncology Group (ECOG) Performance Status of ≤ 2. Life expectancy of at least 3 months as per investigator's judgment at time of screening  Hematological function without transfusion support as follows:  Absolute neutrophil count ≥ 1.0 x 10^9/L (without growth factor support) Platelet count ≥ 50 x 10^9/L (without transfusions within 7 days from screening assessment) Hemoglobin ≥ 8.0 g/dL (transfusions permitted no later than 48 hours before screening) Renal function as follows:  Calculated or measured creatinine clearance ≥ 30 mL/min using:  The Cockcroft-Gault equation OR  Via 24-hour urine collection with plasma and urine creatinine concentrations  Hepatic function as follows: Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 x upper limit of normal (ULN)  Total bilirubin (TBIL) < 1.5 x ULN (unless considered due to Gilbert's syndrome)  Cardiac function as follows:  Left ventricular ejection fraction ≥ 50% as assessed by transthoracic echocardiogram (TTE) or multigated acquisition (MUGA) scan.  Serum sodium, potassium, phosphorus, calcium, and magnesium must be within normal range or if outside normal range must have resolved to Common Terminology Criteria for Adverse Events (CTCAE) version 5.0 grade 1 within 7 days of day 1. Participants not meeting these inclusion criteria may be treated with replacement therapy and re-screened up to 2 times at the discretion of the investigator. Participants with prior COVID-19 infection or history of cardiovascular disease including coronary artery disease, significant valvular disease, cardiac arrhythmia, cardiomyopathy, or history of cardiac toxicity with prior therapy must have a cardiology consultation during screening with a clinical management plan during cytokine release syndrome (CRS) prior to cycle 1 day 1 therapy. Participants with a history of COVID-19 infection must be discussed with the medical monitor prior to enrollment. Participants with a history of COVID-19 infection must have a negative quantitative polymerase chain reaction (PCR) test prior to enrollment.  Exclusion Criteria:  Known central nervous system involvement by multiple myeloma. Recent history of primary plasma cell leukemia (within last 6 months prior to enrollment) or evidence of primary or secondary plasma cell leukemia at the time of screening. Waldenström macroglobulinemia, POEMS syndrome (polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, skin changes), or amyloidosis (participants with multiple myeloma with asymptomatic amyloid plaques found on biopsy would be eligible if all other criteria are met).  History or evidence of any of the following cardiovascular disorders:  Active congestive heart failure (New York Heart Association Class III to IV) Symptomatic ischemia Uncontrolled arrhythmias Screening ECG with corrected QT interval (QTc) of > 470 msec Myocardial infarction within 12 months prior to study day 1  History of malignancy other than multiple myeloma within the past 3 years with the following exceptions:  Malignancy treated with curative intent and with no known active disease present for at least 1 year before enrollment and felt to be at low risk for recurrence by the treating physician. Adequately treated cervical carcinoma in situ without evidence of disease. Breast ductal carcinoma in situ with full surgical resection (ie, negative margins) and without evidence of disease Prostate cancer with a Gleason score < 7 with undetectable prostate specific antigen over 12 months Treated medullary or papillary thyroid cancer Adequately treated urothelial papillary noninvasive carcinoma or carcinoma in situ Similar neoplastic conditions with an expectation of > 95% 5-year disease-free survival Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease. Clinically uncontrolled chronic or ongoing bacterial, fungal, viral, or other infectious disease at study day 1 or within 14 days before study day 1. Positive result for human immunodeficiency virus (HIV).  Active hepatitis B and C based on the following results:  Positive for hepatitis B surface antigen (HepBsAg) (indicative of chronic hepatitis B or recent acute hepatitis B) Negative HepBsAg and positive for hepatitis B core antibody: Either a positive hepatitis B surface antibody or a negative hepatitis B virus DNA by PCR result is necessary for enrollment Positive hepatitis C virus antibody: Negative hepatitis C virus RNA by PCR result is necessary for enrollment Unresolved toxicities from prior anticancer therapy, defined as not having resolved to CTCAE version 5.0 grade 1 or to levels dictated in the eligibility criteria with the exception of grade 2 peripheral neuropathy, alopecia or toxicities from prior anticancer therapy that are considered irreversible (defined as having been present and stable for > 4 weeks) which may be allowed if they are not otherwise described in the exclusion criteria and there is agreement to allow by both the investigator and Amgen medical monitor. Known hypersensitivity to immunoglobulins. Current autoimmune disease that is not well-controlled. Past history or current significant inflammatory neuropathy such as Guillain-Barré syndrome, Chronic inflammatory demyelinating polyradiculoneuropathy, or Multifocal motor neuropathy.  Previously received an allogeneic stem cell transplant and the occurrence of 1 or more of the following:  Received the transplant within 6 months prior to study day 1 Received immunosuppressive therapy within the last 3 months prior to study day 1 Any active acute graft versus host disease (GvHD) requiring systemic therapy within the last 4 weeks prior to start of study treatment Any systemic therapy against GvHD within 4 weeks prior to start of investigational product treatment Autologous stem cell transplantation less than 90 days prior to study day 1. Last non-antibody anticancer treatment (chemotherapy, IMiD, PI, molecular targeted therapy) < 2 weeks and last anticancer therapeutic antibody < 4 weeks prior to study day 1. Lymphodepleting chemotherapy (eg, fludarabine, cyclophosphamide, or anti-CD52 antibody in association with chimeric antigen-receptor T-cell therapy) < 3 months prior to study day 1. Radiation therapy to multiple anatomic sites within 28 days prior to study day 1. Focal radiotherapy within 14 days prior to study day 1. Treatment with systemic immune modulators including, but not limited to, non-topical systemic corticosteroids (unless the dose is less ≤ 10 mg/day prednisone or equivalent), cyclosporine, and tacrolimus within 2 weeks before study day 1. Currently receiving treatment in another investigational device or drug study, or less than 30 days since ending treatment on another investigational device or drug study. Other investigational procedures while participating in this study are excluded. Administration of bone preserving therapies (including bisphosphonates) within 14 days of cycle 1 day 1. Major surgery defined as surgery requiring general anesthesia with endotracheal intubation within 28 days prior to study day 1, unless discussed with and eligibility approved by Amgen medical monitor. Female participants of childbearing potential unwilling to use protocol specified method of contraception during treatment and for an additional 75 days after the last dose of AMG 701. Female participants who are breastfeeding or who plan to breastfeed while on study through 75 days after the last dose of AMG 701. Female participants planning to become pregnant while on study through 75 days after the last dose of AMG 701. Female participants with a positive pregnancy test. Male participants with a female partner of childbearing potential who are unwilling to practice sexual abstinence (refrain from heterosexual intercourse) or use contraception during treatment and for an additional 135 days after the last dose of AMG 701. Male participants unwilling to abstain from donating sperm during treatment and for an additional 135 days after the last dose of AMG 701. Participant likely to not be available to complete all protocol-required study visits or procedures, and/or to comply with all required study procedures (eg, Clinical Outcome Assessments) to the best of the participant and investigator's knowledge. History or evidence of any other clinically significant disorder, condition, or disease (with the exception of those outlined above) that, in the opinion of the investigator or Amgen physician, if consulted, would pose a risk to participant safety or interfere with the study evaluation, procedures or completion.