Copper 64Cu-DOTA-Daratumumab Positron Emission Tomography in Diagnosing Patients With Relapsed Multiple Myeloma

Inclusion Criteria: * All subjects must have the ability to understand and the willingness to sign a written informed consent * Histologically confirmed multiple myeloma (newly diagnosed or relapsed)(Note: multiple myeloma patients with secondary amyloidosis are eligible) * Ability to undergo standard PET imaging; an 18 F FDG PET/CT scan will take place within 3 months of enrollment * Karnofsky performance status \> 70% * Absolute neutrophil count (ANC) \>= 1000/mm\^3 * Platelet count \>= 50/mm\^3; platelet transfusions to help patients meet eligibility criteria are not allowed within 7 days before study enrollment * Total bilirubin =\< 1.5 x the upper limit of normal (ULN) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 3 x ULN * Calculated creatinine clearance \>= 30 mL/min * Woman of childbearing potential must be practicing a highly effective method of birth control consistent with local regulations regarding the use of birth control methods for subjects participating in clinical studies: e.g., established use of oral, injected or implanted hormonal methods of contraception; placement of an intrauterine device or intrauterine system; barrier methods; condom with spermicidal foam/gel/film/cream/suppository or occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/suppository; male partner sterilization; true abstinence (when this is in line with the preferred and usual lifestyle of the subject) during and after the study (6 months after the last dose of 64 Cu-anti-CD38 \[daratumumab\]-NHS-DOTA for women) * A man who is sexually active with a woman of childbearing potential and has not had a vasectomy must agree to use a barrier method of birth control, e.g., either condom with spermicidal foam/gel/film/cream/suppository or partner with occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/suppository, and all men must also not donate sperm during the study and for 6 months after receiving the last dose of study drug Exclusion Criteria: * Daratumumab or other anti CD38 antibody treatment within 3 months prior to study enrollment * Female patients who are lactating or have a positive pregnancy test during the screening period * Major surgery within 14 days prior to start of study treatment * Infection requiring systemic antibiotic therapy within 14 days prior to start of study treatment * Subject is receiving concurrent chemotherapy or biologic or hormonal therapy for cancer treatment; subject is receiving bone marrow stimulatory factors (e.g., granulocyte-macrophage colony-stimulating factor \[GM-CSF\]); Note: Concurrent use of hormones for noncancer-related conditions (e.g., insulin for diabetes) is acceptable * Vaccination with live attenuated vaccines within 4 weeks of study agent administration * Subject is currently using or has used immunosuppressive medication within 14 days prior to the study agent administration; the following are exceptions: * Intranasal, topical, inhaled, or local steroid injections (e.g., intra-articular injection) * Chronic systemic corticosteroids at physiologic doses not to exceed 10 mg/day of prednisone or equivalent * Steroids as premedication for hypersensitivity reactions (e.g., infusion-related reactions, CT scan premedication) * Subject has plasma cell leukemia, Waldenstrom's macroglobulinemia, POEMS syndrome (polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and skin changes), or primary amyloidosis * Subject has known chronic obstructive pulmonary disease (COPD) with a forced expiratory volume in 1 second (FEV1) \< 50% predicted normal; Note that FEV1 testing is required for patients suspected of having COPD and subjects must be excluded if FEV1 \< 50% * Subject has known allergies, hypersensitivity, or intolerance to monoclonal antibodies or human proteins, or their excipients (refer to respective package inserts or investigator's brochure) * Subject has history of primary immunodeficiency * Subject is positive for human immunodeficiency virus (HIV-1), chronic or active hepatitis B, or active hepatitis A or C * Subject has any one of the following: * Clinically significant abnormal electrocardiography (ECG) finding at screening * Congestive heart failure (New York Heart Association class III or IV) * Myocardial infarction within 12 months prior to starting study treatment * Unstable or poorly controlled angina pectoris, including Prinzmetal variant angina pectoris * Subject has presence of other active malignancy (see exceptions below) (However, research participants with history of prior malignancy treated with curative intent and in complete remission are eligible). The following malignancies are exceptions to the active malignancy statement: * Basal cell carcinoma of the skin * Squamous cell carcinoma of the skin * Carcinoma in situ of the cervix * Carcinoma in situ of the breast * Incidental histologic finding of prostate cancer (T1a or T1b using the TNM clinical staging system) or prostate cancer that is curative * 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)