The following criteria is provided for health care professionals.

For Parts 1 and 2:

• Has MM defined by the IMWG criteria with evidence of disease progression and:
  • In need of additional myeloma therapy as determined by the investigator.
  • Has previously received at least 3 lines of myeloma therapy (for example, containing an Immunomodulatory imide drug [IMiD], a proteasome inhibitor [PI], an alkylating agent, and/or an anti-CD38 as single agents or in combination).
  • Is either refractory to or intolerant of at least 1 PI and a least 1 IMiD.

For Part 3:

• Has MM defined by the IMWG criteria with evidence of disease progression and:
  • In need of additional myeloma therapy as determined by the investigator.
  • Has previously received at least 3 lines of myeloma therapy.
  • Is refractory to at least 1 IMiD (ie, lenalidomide or pomalidomide [thalidomide excluded]), at least 1 PI (ie, bortezomib, ixazomib, or carfilzomib), and refractory to at least 1 anti-CD38 antibody (ie, daratumumab or isatuximab) and has demonstrated disease progression with the last therapy. Participants who are primary refractory, meaning they never achieved at least a MR with any previous treatment line, are not eligible.
• For participants in Part 2 and 3 only: Measurable disease is defined as :
  • Serum M-protein ≥500 mg/dL (≥5 g/L)
  • Urine M-protein ≥200 mg/24 hours.
  • Serum free light chain (FLC) assay, with involved FLC level ≥10 mg/dL (≥100 mg/L) provided serum FLC ratio is abnormal.
• During Part 1 only, participants not meeting the above criteria for measurable disease should, at least, have measurable bone marrow plasmacytosis (greater than or equal to [≥ ] 10 percent [%]) and/or plasmacytoma (≥1 centimeter [cm] in diameter) detected by physical examination or imaging.
• Eastern Cooperative Oncology Group (ECOG) performance status of ≤2.
• Has MM defined by the IMWG criteria with evidence of disease progression and:
  • In need of additional myeloma therapy as determined by the investigator.
  • Has previously received at least 3 lines of myeloma therapy (example, containing an Immunomodulatory imide drug [IMid], a proteasome inhibitor [PI], an alkylating agent, and/or an anti-CD38 as single agents or in combination).
  • Has either refractory to or intolerant of at least one proteasome inhibitor and a least one immunomodulatory drug.
• For participants in MTD/OBD cohort expansion and Phase 2 only: participant has measurable disease.
• During dose escalation only, participants not meeting the above criteria for measurable disease should, at least, have measurable bone marrow plasmacytosis (greater than or equal to [>=] 10 percent [%]) and/or plasmacytoma (>=1 centimeter [cm] in diameter) detected by physical examination or imaging.
• Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1.

Exclusion Criteria:

For Parts 1 and 2:

• Has polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and skin changes (POEMS) syndrome, monoclonal gammopathy of unknown significance, smoldering myeloma, solitary plasmacytoma, amyloidosis, Waldenstrom macroglobinemia macroglobulinemia or immunoglobulin M (IgM) myeloma, or lymphoplasmacytic lymphoma (LPL).
• Has sensory or motor neuropathy of NCI CTCAE >=Grade 3.
• Who have received autologous stem cell transplant (SCT) 60 days before first infusion of TAK-573 modakafusp alfa or participants who have received allogeneic SCT 6 months before first infusion. Graft-versus-host disease that is active or requires ongoing systemic immunosuppression.
• Has not recovered from adverse reactions to prior myeloma treatment or procedures (chemotherapy, immunotherapy, radiation therapy) to NCI CTCAE less than or equal to ( <= ≤) Grade 1 or baseline, except for sensory or motor neuropathy which should have recovered to <= ≤ Grade 2 or baseline.
• Has clinical signs of central nervous system involvement of MM.

For Part 3:

• Hepatitis B virus (HBV) or hepatitis C virus (HCV) infection. Seropositive for hepatitis B (defined by a positive test for hepatitis B surface antigen [HBsAg]. Participants with resolved infection (that is, participants who are HBsAg negative but positive for antibodies to hepatitis B core antigen [anti-HBc] and/or antibodies to hepatitis B surface antigen [anti-HBs]) must be screened using real-time polymerase chain reaction (PCR) measurement of HBV DNA levels. Those who are PCR positive will be excluded.
• In addition to the above criteria, participants must not have plasma cell leukemia or have had primary refractory MM, current central nervous system involvement of MM, myelodysplastic syndrome, myeloproliferative syndrome, or have had a second malignancy within the previous 3 years, except treated basal cell or localized squamous skin carcinomas, localized prostate cancer, cervical carcinoma in situ, resected colorectal adenomatous polyps, breast cancer in situ, or other malignancy for which the participant is not on active anticancer therapy.