Inclusion Criteria:

• Be willing and able to provide signed informed consent for the trial.
• Age ≥18 years at the time of signed consent.
• ECOG Performance Status ≤2.
• Have histologically-confirmed NHL or MM that has relapsed from or is refractory to prior therapy, and should not be candidates for regimens known to provide clinical benefit or should have refused such treatment options
  • MM subjects must have:
  • Measurable disease at baseline defined as:
    • Serum M protein ≥0.5g/dL; or
    • Urine M protein ≥200mg/24-hour; or
    • For subjects without measurable serum or urine M protein, serum FLC >100 mg/L and an abnormal (κ/λ) ratio
  • For subjects with (IgA), myeloma whose disease can only be reliably measured by quantitative immunoglobulin measurement, a serum IgA level ≥ 0.50g/dL.
• Received at least 3 prior treatment regimens including lenalidomide, pomalidomide, a proteasome inhibitor, a glucocorticoid and an anti-CD38 antibody.
• Refractory to, or had documented disease progression within 60 days from the last dose of their prior MM treatment (or, if the last MM therapy was with CAR-T cells, documented disease progression any time after administration).
• NHL subjects must have:
  • Documented diagnosis of NHL and measurable disease defined by measurable disease (consistent with Lugano classification)
  • NHL subjects must have received the following regarding prior therapy:
  • Peripheral T-cell Lymphoma: At least one prior line containing alkylator-based chemotherapy. Note: For subjects with Anaplastic Large Cell Lymphoma (ALCL), the subject must also have received CD30 antibody therapy.
  • Mantle Cell Lymphoma: ≥2 lines of therapy, including CD20 antibody and alkylator chemotherapy, and a Bruton's tyrosine kinase (BTK) inhibitor.
  • Follicular Lymphoma: ≥2 lines of therapy, including CD20 antibody therapy and alkylator chemotherapy.
  • Diffuse Large B-cell Lymphoma: ≥2 lines of therapy, including prior CD20 antibody therapy, and has received prior autologous bone marrow transplant (or is ineligible for bone marrow transplant).
  • Other NHL: Subjects must have been treated or refused treatment with any standard of care therapies known to provide clinical benefit.
• In Phase 2, only subjects with the following indications will be eligible for the appropriate expansion arm:
  • Relapsed/refractory MM (as defined in Phase 1 of the study).
  • Relapsed/refractory T-cell NHL including: PTCL, PTCL-NOS, AITL and ALCL with relapsed refractory disease following 1 prior line of therapy containing alkylator-based chemotherapy will be included. Subjects with ALCL must have had prior exposure to anti CD30 antibody as part of their prior treatment regimen.
• Have provided archival tumor tissue sample or newly obtained core or excisional biopsy of a tumor lesion (lymph node or extra-nodal infiltration of a tissue for NHL subjects, bone marrow aspirate and biopsy for MM subjects) and for Adult T-cell leukemia/lymphoma (ATLL) subjects [if applicable], not previously irradiated.
• Subjects need to have adequate organ function defined as follows to include:
  • ANC ≥1.0 x 109/L
  • Platelets ≥75,000 cells/µL
  • Hemoglobin ≥8.0 g/dL
  • ALT and AST ≤3.0 x upper limit of normal (ULN); except for subjects who have tumor infiltration of the liver, where ALT or AST ≤5 x ULN.
  • Total bilirubin ≤1.5 x ULN (unless due to Gilbert's syndrome).
  • CrCl ≥40 mL/min
  • International normalized ratio (INR) <1.5 x ULN and aPTT <1.5 x ULN (subject receiving anticoagulant therapy must be on a stable regimen)
• Female subjects may not be pregnant or intend to become pregnant, may not breastfeed or intend to breastfeed, or donate ova, and must satisfy one of the following conditions:
  • A woman of childbearing potential (WOCBP) must agree to use highly effective contraception during study participation and 30 days after the completion of study treatment.
  • A woman on hormone replacement therapy (HRT) and whose menopausal status is in doubt will be required to use one of the contraception methods specified if they wish to continue their HRT during the study
  • A woman of non-childbearing potential (i.e., physiologically incapable of becoming pregnant) or postmenopausal
• A male subject must agree to use a condom when having intercourse with a person of child bearing potential during the treatment period and for at least 30 days after the last dose of study treatment.
• Males must refrain from donating sperm during the treatment period and for 30 days after the last dose of study treatment.
• Subjects must refrain from donating blood during study treatment and for 30 days after discontinuation.

Exclusion Criteria:

• Presence of central nervous system (CNS) disease.
• Has received prior radiotherapy within 2 weeks of start of study treatment.
• Have active pneumonitis.
• Have any of the following:
  • Non-secretory or oligosecretory MM
  • Plasma cell leukemia
  • Systemic light chain amyloidosis
  • Polyneuropathy, Organomegaly, Endocrinopathy, Monoclonal gammopathy, and Skin changes (POEMS) Syndrome
  • Lymphoblastic lymphoma
  • Mycosis fungoides
  • Sezary syndrome
  • Primary cutaneous T-cell lymphomas
  • B-cell or T-cell prolymphocytic leukemia
  • Chronic lymphocytic lymphoma/small cell lymphoma
  • Richter's transformation
  • Burkitt lymphoma
  • Myelodysplastic syndrome
• Have received prior CC92480 (mezigdomide) during the subjects most recent line of therapy
• Subjects with a peripheral neuropathy ≥ Grade 2 at screening.
• Clinically significant impaired cardiac function or clinically significant cardiac disease, including any of the following:
  • Clinically significant and/or uncontrolled heart disease such as congestive heart failure requiring treatment (NYHA ≥Grade 2), uncontrolled hypertension, or clinically significant arrhythmia.
  • Interval corrected according to Friderica's correction (QTcF) >480 msec on screening ECG.
  • Acute myocardial infarction or unstable angina pectoris within 6 months prior to study entry.
• Thromboembolic event occurring within 3 months of the first dose of cemsidomide. Enrolled subjects must have a risk-based prophylaxis for venous thromboembolism.
• Known malignancy other than study indication that has progressed or has required treatment within the past 3 years.
• Major surgery within 2 weeks of the first dose of study treatment.
• Presence of ≥Grade 2 toxicity (CTCAE v5.0) due to prior cancer therapy.
• Received live, attenuated vaccine within four weeks of first dose.
• Known history of human immunodeficiency virus (HIV) infection. No HIV testing is required unless mandated by local health authority.
• Any Subject with a known history of, or considered at risk for, Hepatitis B infection must be tested. Subjects will be excluded if Hepatitis B surface antigen (HBS-Ag) is detected
• Any Subject with a known history or risk of Hepatitis C virus must test negative for anti-HCV antibodies. If anti-HCV antibodies are present or there is prior history of HCV treatment, HCV RNA must be undetectable.
• Uncontrolled active systemic infection or any life-threatening illness, medical condition, or organ system dysfunction which, in the investigator's opinion, could compromise the subject's safety or put the study outcomes at undue risk.
• Concurrent administration of strong CYP3A modulators (inducers or inhibitors, including certain foods) and inhibitors of MDR1 (p-glycoprotein) and BCRP. Strong CYP3A inhibitors and inhibitors of MDR1 and BCFP must be discontinued 5 half-lives before the first dose of study drug, and strong CYP3A inducers must be discontinued 14 days prior to the first dose of study drug.
• Is currently participating in, or has participated in, a study of an investigational agent, or has used an investigational treatment within ≤ 5 half-lives or within 4 weeks (whichever is shorter) prior to the first dose of study treatment.
• Inability or difficulty swallowing capsules, or tablets (as available), malabsorption syndrome, or any disease or medical condition significantly affecting gastrointestinal function.
• Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound results of the study, interfere with the subject's participation for full duration of the study, or is not in the best interest of the subject to participate, in the opinion of the treating investigator.
• Has a known psychiatric or substance abuse disorder that would interfere with cooperating with requirements of the study.
• Previously identified hypersensitivity to components of the study treatment or excipients.