Inclusion Criteria - Part 1:

• With a confirmed diagnosis of multiple myeloma (MM). 
• With RRMM who have failed treatment with, are intolerant to, or are not candidates for available therapies that are known to confer clinical benefit in this participant population. 
• Should meet all of the following criteria for prior therapy: 
  • Should be refractory to at least one proteasome inhibitor (PI), at least one immunomodulatory drug (IMiD), and at least 1 steroid. 
  • Should either have received ≥ 3 prior lines of therapy or should have received at least two prior lines of therapy if one of those lines included a combination of PI and IMiD. 
  • Prior treatment with an anti-CD38 therapy (including daratumumab) is permitted. 
• With measurable disease, defined as at least 1 of the following:
  • Serum M-protein ≥ 500 mg/dL (≥ 5 g/L) on serum protein electrophoresis (SPEP).
  • Urine M-protein ≥ 200 mg/24 h on urine protein electrophoresis (UPEP). 
  • Serum FLC assay result with an involved FLC level ≥ 10 mg/dL (≥ 100 milligram per liter [mg/L]), provided the serum FLC ratio is abnormal. 
• Eastern Cooperative Oncology Group (ECOG) performance status score of 0 or 1. 
• With normal QT interval corrected by the Fridericia method (QTcF) on screening electrocardiogram (ECG), defined as QTcF of ≤ 450 millisecond (ms) in males or ≤ 470 ms in females.
• Must meet the following clinical laboratory criteria at study entry: 
  • Total bilirubin ≤ 1.5*the upper limit of the normal range (ULN), except for participant with Gilbert's syndrome, in whom the direct bilirubin must be < 2.0*ULN. 
  • Serum alanine aminotransferase (ALT) and aspartate aminotransferase (AST) must be ≤ 2.5*ULN. 
  • Estimated glomerular filtration rate (eGFR) ≥ 30 milliliters per minute (mL/min/1.73 square meter [m^2], using the modification of diet in renal disease (MDRD) equation. 
  • Absolute neutrophil count (ANC) ≥ 1000 per cubic millimeter (/mm^3) (≥ 1.0*10^ 9 per liter [/L]); a count of ≥ 750/mm^3 (≥ 0.75*10^ 9/L) may be acceptable for participants with > 50% of plasma cells in bone marrow, after discussion with the sponsor. 
  • Platelet count ≥ 75,000/ mm^3 (≥ 75*10^ 9/L); a value of ≥ 50,000/ mm^3 (≥ 50*10^ 9/L) may be acceptable for participants with > 50% of plasma cells in bone marrow, after discussion with the sponsor. 
  • Hemoglobin ≥ 7.5 g/dL (it is not permissible to transfuse a participant to reach this level).

Inclusion Criteria - Part 2:

• With a confirmed diagnosis of multiple myeloma (MM). 
• Should meet all of the following criteria for prior therapy:
  • Should be refractory or intolerant to at least 1 PI and at least 1 IMiD;
  • Should either have received ≥ 3 prior lines of therapy or should have received at least 2 prior lines of therapy if 1 of those lines included a combination of PI and IMiD;
  • Prior treatment with an anti-CD38 therapy (including daratumumab) is permitted, except for participants enrolled into the anti-CD38-therapy naïve expansion cohort;
  • Daratumumab-RR cohorts (once weekly and once every two weeks TAK-169 dosing).  Participant must be RR to daratumumab at any time during treatment. Of note, participant's RR to other anti-CD38 therapies are excluded;
  • Anti-CD38 Therapy Naïve cohort (once weekly dosing).  Participants must not have received any prior anti-CD38 therapy.
• With measurable disease, defined as at least 1 of the following: 
  • Serum M-protein ≥ 500 mg/dL (≥ 5 g/L) on SPEP. 
  • Urine M-protein ≥ 200 mg/24 hours on UPEP. 
  • Serum FLC assay result with an involved FLC level ≥ 10 mg/d (≥ 100 mg/L), provided the serum FLC ratio is abnormal
• ECOG performance status score of 0 or 1.
• With normal QTcF on screening ECG, defined as QTcF of ≤ 450 ms in males or ≤ 470 ms in females
• Must meet the following clinical laboratory criteria at study entry: 
  • Total bilirubin ≤ 1.5*the ULN, except for participant with Gilbert's syndrome, in whom the direct bilirubin must be < 2.0*ULN;
  • Serum ALT and ASTmust be ≤ 2.5*ULN. - eGFR ≥ 30 mL/min/1.73 m^2, using the MDRD equation;
  • ANC ≥ 1000 mm^3 (≥ 1.0*10^ 9 /L); a count of ≥ 750/mm^3 (≥ 0.75*10^ 9/L) may be acceptable for participant with > 50% of plasma cells in bone marrow, after discussion with the sponsor; 
  • Platelet count ≥ 75,000/ mm^3 (≥ 75*10^ 9/L); a value of ≥ 50,000/ mm^3 (≥ 50*10^ 9/L) may be acceptable for participants with > 50% of plasma cells in bone marrow, after discussion with the sponsor; 
  • Hemoglobin ≥ 7.5 g/dL (it is not permissible to transfuse a participant to reach this level).

Exclusion Criteria:

• Patients with polyneuropathy, organomegaly, endocrinopathy, monoclonal gammopathy and skin changes (POEMS) syndrome, monoclonal gammopathy of unknown significance, smoldering myeloma, solitary plasmacytoma, amyloidosis, Waldenström macroglobulinemia, or Immunoglobulin M (IgM) myeloma.
• Patients with sensory or motor neuropathy of NCI CTCAE Grade ≥ 3.
• Patients who have received a final dose of any of the following treatments/procedures within the following minimum interval before the first dose of TAK-169: 
  • Myeloma-specific therapy, including PIs and IMiDs (14 days); 
  • Anti-CD38 (a) therapy (Once the MTD/RP2D has been established, the washout period may be adjusted in the expansion phase (Part 2) of the study for participants who have received anti-CD38 therapy )(90 days);
  • Corticosteroid therapy for myeloma (7 days); 
  • Radiation therapy for localized bone lesions (14 days); 
  • Major surgery (30 days); 
  • Autologous stem cell transplant (90 days);
  • Investigational therapy (30 days).
• Patients who have received an allogeneic stem cell transplant or organ transplantation.
• Patients who have not recovered, to NCI CTCAE V5 Grade ≤ 1 or baseline, from adverse reactions to prior myeloma treatment or procedures (chemotherapy, immunotherapy, radiation therapy) excluding alopecia.
• Patients with clinical signs of central nervous system (CNS) involvement of MM.
• Patients with known or suspected light chain amyloidosis of any organ (the presence of amyloid on the bone marrow biopsy without other evidence of amyloidosis is acceptable).
• Patients with congestive heart failure (New York Heart Association) class ≥ II or LVEF (left ventricular ejection fraction) < 40%, cardiac myopathy, active ischemia, or any other uncontrolled cardiac condition such as angina pectoris or myocardial infarction within the past 6 months, clinically significant arrhythmia requiring therapy including anticoagulants, or clinically significant uncontrolled hypertension. Patients are also excluded if cardiac MRI demonstrates evidence of infiltrative disease of the myocardium, such as amyloid cardiomyopathy.
• Patients with chronic or active infection requiring systemic therapy, as well as a history of symptomatic viral infection that has not been fully cured (example, human immunodeficiency viruses (HIV) or viral hepatitis B or C).
• Patients with a history of systemic inflammatory response syndrome (SIRS)/ cytokine release syndrome (CRS) reactions following infusion with any monoclonal antibodies or Chimeric Antigen Receptor (CAR) T-cell therapy
• Patients with a chronic condition requiring the use of systemic corticosteroids at a dose of > 10 milligram per day (mg/day) of prednisone or equivalent.