Inclusion Criteria:

* Documented informed consent of the participant and/or legally authorized representative

* Assent, when appropriate, will be obtained per institutional guidelines
* Agreement to allow the use of archival tissue from diagnostic tumor biopsies

* If unavailable, exceptions may be granted with study principal investigator (PI) approval
* Age: ≥ 18 years
* Karnofsky performance status (KPS) ≥ 60%
* Diagnosis of multiple myeloma with extramedullary disease (EMD). EMD is defined as soft-tissue plasmacytomas NOT arising from skeletal lesions (i.e., the EMD is not contiguous with any bone/bony lesion)
* Measurable systemic disease defined as serum M-spike ≥ 0.5 g/dl, 24-hour urine M-spike ≥ 200 mg/24 hours (hr), involved serum free light chain (FLC) ≥ 10 mg/dl with abnormal FLC ratio, and/or a non-target plasmacytoma ≥ 2 cm in a single diameter (NOTE: Non-target plasmacytoma must not be included in the EMD-EBRT field)
* At least one site of EMD must have an indication for palliative radiation per the treating clinicians (e.g., including but not limited to pain, asymmetry, discomfort, threatening to vital structure, etc.)
* Target EMD site must be encompassed by one radiation field per treating radiation oncologist
* Subject must have received an immunomodulatory agent, a proteasome inhibitor, and an anti-CD38 antibody
* Fully recovered from the acute non-hematologic toxic effects (except alopecia) to ≤ grade 1 to prior anti-cancer therapy
* Prior antitumor therapy must have been completed prior to enrollment as follows:

* ≥ 2 weeks for prior external beam radiotherapy (XRT) to non-target site
* ≥ 21 days for cytotoxic chemotherapy (systemic or intrathecal)
* ≥ 28 days for prior adoptive cell therapy or T-cell redirecting therapies
* ≥ 4 weeks or 5 half-lives (whichever is shorter) for other myeloma therapies
* Absolute neutrophil count (ANC) ≥ 1,000/mm\^3 (prior growth factor support is permitted but must be without support for 7 days for granulocyte colony-stimulating factor \[G-CSF\] or granulocyte-macrophage colony-stimulating factor \[GM-CSF\] and for 14 days for pegylated GCSF before the laboratory test)

* Two repeat tests are allowed. If the repeat test satisfies criteria, the participant may enroll provided all other criteria are met
* Platelets ≥ 50,000/mm\^3

* NOTE: No transfusion support or thrombopoietin receptor agonist within 7 days before laboratory test
* Two repeat tests are allowed. If the repeat test satisfies criteria, the participant may enroll provided all other criteria are met
* Hemoglobin ≥ 8g/dL

* NOTE: No transfusion support or erythropoietin use within 7 days before the laboratory test
* Two repeat tests are allowed. If the repeat test satisfies criteria, the participant may enroll provided all other criteria are met
* Total bilirubin ≤ 2.0 X upper limit of normal (ULN) (unless has congenital bilirubinemia such as Gilbert's disease, in which case ≤ 1.5 × ULN is required)

* Two repeat tests are allowed. If the repeat test satisfies criteria, the participant may enroll provided all other criteria are met
* Aspartate aminotransferase (AST) ≤ 2.5 x ULN

* Two repeat tests are allowed. If the repeat test satisfies criteria, the participant may enroll provided all other criteria are met
* Alanine aminotransferase (ALT) ≤ 2.5 x ULN

* Two repeat tests are allowed. If the repeat test satisfies criteria, the participant may enroll provided all other criteria are met
* Creatinine clearance of ≥ 30 mL/min per 24 hour urine test or the Cockcroft-Gault formula

* Two repeat tests are allowed. If the repeat test satisfies criteria, the participant may enroll provided all other criteria are met
* Women of childbearing potential (WOCBP): negative urine or serum pregnancy test

* If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required
* Two repeat tests are allowed. If the repeat test satisfies criteria, the participant may enroll provided all other criteria are met
* Agreement by females and males of childbearing potential to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 6 months after the last dose of talquetamab

* Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only)

Exclusion Criteria:

* Prior irradiation to target EMD site or field
* Prior GPRC5D therapy
* Prior radiopharmaceutical therapy
* Patients who have received previous radiation to \> 25% of their bone marrow
* Prior allogeneic hematopoietic cell transplantation within the past 6 months or prior autologous hematopoietic cell transplantation within the past 12 weeks
* A maximum cumulative dose of corticosteroids of ≥ 140 mg of prednisone or equivalent within 14-day period before the first dose of study drug (does not include pre-treatment medications)
* Major surgery within 2 weeks prior to the start of administration of study treatment, or will not have fully recovered from surgery, or has major surgery planned during the time the participant is expected to be treated in the study, or within 2 weeks after administration of the last dose of study treatment

* Note: Participants with planned surgical procedures to be conducted under local anesthesia may participate. Kyphoplasty or vertebroplasty are not considered major surgery. If there is a question whether a procedure is considered a major surgery, the investigator must consult with the appropriate representative at Janssen and resolve any issues before enrolling a participant in the study
* Ongoing or active infection
* Severe persistent asthma or severe chronic obstructive pulmonary disease (COPD)
* Presence of the following cardiac conditions:

* New York Heart Association stage III or IV congestive heart failure
* Myocardial infarction or coronary artery bypass graft ≤ 6 months prior to randomization
* Uncontrolled cardiac arrhythmia or clinically significant electrocardiogram (ECG) abnormalities
* History of clinically significant ventricular arrhythmia or unexplained syncope, not believed to be vasovagal in nature or due to dehydration
* History of severe non-ischemic cardiomyopathy
* Any of the following:

* Hepatitis B infection (i.e., hepatitis B virus surface antigen \[HBsAg\] or hepatitis B virus \[HBV\]-deoxyribonucleic acid \[DNA\] positive). In the event the infection status is unclear, quantitative viral levels are necessary to determine the infection status
* Active hepatitis C infection as measured by positive hepatitis C virus \[HCV\]-ribonucleic acid \[RNA\] testing. Participants with a history of HCV antibody positivity must undergo HCV-RNA testing. If a participant with history of chronic hepatitis C infection (defined as both HCV antibody and HCV-RNA positive) completed antiviral therapy and has undetectable HCV-RNA for at least 12 weeks following the completion of therapy, the participant is eligible for the study
* Plasma cell leukemia (\> 20% circulating plasma cells and/or \> 2.0 x 10\^9/L plasma cells) at the time of screening, Waldenström's macroglobulinemia, POEMS syndrome (polyneuropathy, organomegaly, endocrinopathy, M-protein, and skin changes), or primary amyloid light chain amyloidosis
* Known active central nervous system (CNS) involvement or exhibits clinical signs of meningeal involvement of multiple myeloma. If either is suspected, negative whole brain MRI and lumbar cytology are required
* Other active malignancy. Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial
* Stroke or seizure within 6 months prior to enrollment
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agent
* If HIV positive, any of the following:

* Detectable viral load at screening
* CD4+ T cell count ≤ 300
* AIDS-defining opportunistic infection within 6 months of screening
* Changes in highly active antiretroviral therapy (HAART) due to resistance/progression that occurred within 3 months prior to screening
* Changes in HAART due to toxicity within 4 weeks prior to screening
* Females only: Pregnant or breastfeeding
* Any other condition that would, in the Investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures
* Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)