The primary purpose of this study is to identify the recommended phase 2 dose (RP2D[s]) and schedule(s) to be safe for JNJ-79635322 in Part 1 (dose escalation), and to characterize the safety and tolerability of JNJ-79635322 at the RP2D(s) selected and in disease subgroups in Part 2 (dose expansion).

Inclusion Criteria:

For participants with relapsed or refractory multiple myeloma:

• Have a documented initial diagnosis of multiple myeloma according to International Myeloma Working Group (IMWG) diagnostic criteria
• Part 1: Have relapsed or refractory disease, have been treated with a proteasome inhibitor, immunomodulatory drug (IMiD) agent, and an anti-CD38-based therapy for the treatment of multiple myeloma (MM),and should have been treated with at least 3 prior lines of therapy, or are refractory to proteosome inhibitor, IMiD agent, and an anti-CD38-based therapy regardless of prior lines of therapy, Part 2: Have relapsed or refractory disease, have been treated with a PI, IMiD and an anti-CD38 based therapy
• Must have an Eastern Cooperative Oncology Group (ECOG) status of 0 or 1
• Have measurable disease at screening as defined by at least 1 of the following: a) Serum M-protein level greater than or equal to (>=) 0.5 grams per deciliter (g/dL); or b) Urine M-protein level >=200 milligrams (mg)/24 hours; or c) Light chain multiple myeloma: Serum immunoglobulin (Ig) free light chain (FLC) >=10 milligrams per deciliter (mg/dL) and abnormal serum Ig kappa lambda FLC ratio; d) For participants without measurable disease in the serum, urine, or involved FLC, presence of 1 or more focus of extramedullary disease (EMD) which meets the following criteria: extramedullary plasmacytoma not contiguous with a bone lesion, at least 1 lesion >=2 centimeter [cm] (at its greatest dimension) diameter on whole body Positron Emission Tomography and Computed Tomography (PET-CT) Scans (or whole body magnetic resonance imaging [MRI] approved by sponsor), and not previously radiated (Part 2C participants are not required to have measurable disease)

For participants with previously treated AL amyloidosis:

• Initial histopathological diagnosis of amyloidosis
• Participant who is not a candidate for available AL amyloidosis therapy with established clinical benefit and should have received at least 3 cycles of 1 prior line of therapy or a total of at least 2 cycles of 2 or more prior lines of therapy for AL amyloidosis
• Measurable disease at screening defined by at least 1 of the following: serum involved free light chain (iFLC) >=50 mg/L or difference between involved and uninvolved free light chains (dFLC) >=50 mg/L, or serum m-protein >= 0.5 g/dL
• One or more organs impacted by systemic AL amyloidosis
• Left ventricular ejection fraction (LVEF) >=45%

Exclusion Criteria:

For participants with relapsed or refractory multiple myeloma:

• Central Nervous System (CNS) involvement or clinical signs of meningeal involvement of multiple myeloma. If either is suspected, brain magnetic resonance imaging (MRI) and lumbar cytology are required
• Active plasma cell leukemia, Waldenstrom's macroglobulinemia, POEMS syndrome (polyneuropathy, organomegaly, endocrinopathy, M-protein, and skin changes), or primary light chain amyloidosis
• Received a cumulative dose of corticosteroids equivalent to greater than (>) 140 mg of prednisone within the 14-day period before the start of study treatment administration
• Prior antitumor therapy as follows, in the specified time frame prior to the first dose of study treatment: (proteasome inhibitor [PI] therapy or radiotherapy within 14 days, immunomodulatory drug (IMiD) agent therapy within 7 days, gene-modified adoptive cell therapy within 90 days [not applicable for Part 2C participants], or CD3-redirecting therapy within 21 days[not applicable for Part 2B or 2C participants])
• Prior allogeneic transplant within 6 months before the start of study treatment administration or autologous transplant within 12 weeks before the start of study treatment administration
• Live, attenuated vaccine within 4 weeks before the first dose of study treatment
• Non-hematologic toxicity from prior anticancer therapy that has not resolved to baseline levels or to Grade less than or equal to (<=) 1 (except alopecia, tissue post-RT fibrosis [any grade] or peripheral neuropathy to Grade <=3)
• The following medical conditions: pulmonary compromise requiring supplemental oxygen use to maintain adequate oxygenation, human immunodeficiency (HIV) infection, active hepatitis B or C infection, stroke or seizure within 6 months prior to first dose of study treatment, autoimmune disease, serious active viral or bacterial infection, uncontrolled systemic fungal infection, cardiac conditions (myocardial infarction <=6 months prior to enrollment, New York Heart Association stage III or IV congestive heart failure, et cetera)
• Part 2C: have progressive disease or refractory disease per IMWG after CAR-T administration

For participants with previously treated AL amyloidosis:

• CNS involvement or clinical signs of meningeal involvement of AL amyloidosis. If either is suspected, whole brain MRI and lumbar cytology are required
• Any form of non-AL amyloidosis, including but not limited to transthyretin (ATTR) amyloidosis
• Active plasma cell leukemia, Waldenstrom's macroglobulinemia, or POEMS syndrome
• Pulmonary compromise requiring supplemental oxygen use
• Any serious medical conditions such as: active viral, bacterial, fungal infection; active autoimmune disease; HIV infection, active hepatitis B or C infection, stroke or seizure within 6 months prior to first dose of study treatment, significant cardiovascular conditions
• Previous or current diagnosis of symptomatic multiple myeloma
• Macroglossia that impairs swallowing difficulty
• Received a cumulative dose of corticosteroids equivalent to > 140 mg of prednisone within the 14-day period before the start of study treatment administration
• Prior antitumor therapy within 21 days prior to the first dose of study treatment (PI therapy or radiotherapy within 14 days, IMiD agent therapy within 7 days, gene-modified adoptive cell therapy within 90 days, or CD3-redirecting therapy within 21 days)
• Prior allogeneic transplant within 6 months before the start of study treatment administration or autologous transplant within 12 weeks before the start of study treatment administration
• Live, attenuated vaccine within 4 weeks before the first dose of study treatment
• Non-hematologic toxicity from prior anticancer therapy that has not resolved to baseline levels or to <=1 (except alopecia, tissue post-RT fibrosis [any grade] or peripheral neuropathy to Grade <=3)

The data sharing policy of the Janssen Pharmaceutical Companies of Johnson & Johnson is available at www.janssen.com/clinical-trials/transparency. As noted on this site, requests for access to the study data can be submitted through Yale Open Data Access (YODA) Project site at yoda.yale.edu