Key Inclusion Criteria:

• Participants must be at least 18 years of age or the legal age of consent in the jurisdiction
• in which the study is taking place;
• Eastern Cooperative Oncology Group performance status of ≤ 2 in module 1, or 0 or 1 in modules 2 and 3;
• Documentation of Multiple Myeloma (MM) as defined by International Myeloma Working Group (IMWG) Diagnostic Criteria for Multiple Myeloma. Site should ensure that Multiple Myeloma diagnosis is confirmed in accordance with the IMWG Diagnostic Criteria;
• Participants must have one or more measurable disease criteria for Serum M-Protein, Urine M-protein, and Serum immunoglobulin free light chains as specified in the relevant module of the CSP;
• Adequate organ and bone marrow function assessment at screening according to the hematological, hepatic, and renal parameters listed in the CSP as relevant to each module;
• Participants must have received at least 3 prior lines of treatment in module 1, or 1-3 prior lines in modules 2 and 3, with additional module-specific requirements related to prior lines of therapy

The above is a summary of key criteria, other inclusion criteria details may apply

Key Exclusion Criteria:

• Amyloidosis, plasma cell leukemia, Waldenstrom Macroglobulinemia, Polyneuropathy Organomegaly Endocrinopathy M-protein and Skin Syndrome, or Smoldering Multiple Myeloma (compliant with WHO criteria);
• Participants exhibiting clinical signs of central nervous system involvement of MM;
• Participants with known COPD, or previous history of ILD/pneumonitis;
• Participants with known moderate or severe persistent asthma within the past 5 years, or uncontrolled asthma of any classification;
• Participants who have severe cardiovascular disease which is not adequately controlled;
• Participants who have a history of immunodeficiency disease;
• Participants with peripheral neuropathy ≥ Grade 2;
• Primary refractory MM;
• Participants who have previously received anti-GPRC5D or MMAE-containing treatment;
• Participants who have previously received allogenic stem cell transplant, or participant has received autologous stem cell transplant within 3 months before the first dose of study intervention;
• Participants with a history of prior malignancy other than MM within 3 years prior to first dose of study intervention. some exceptions apply;
• Participants with previous history of active JC virus infection resulting in PML;
• Participants with a known hypersensitivity to AZD0305 or any of the excipients of the product or to any of the drugs included in the respective modules or who experienced Grade 3 or higher hypersensitivity to prior monoclonal antibody therapy;
• Participants who have uncontrolled severe illness including but not limited to ongoing active infection requiring therapeutic antibiotics and/or other administration

The above is a summary of key criteria, other exclusion criteria details may apply