Testing JNJ-79635322 for patients with advanced multiple myeloma or AL amyloidosis

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)