Inclusion Criteria:
* Eastern Cooperative Oncology Group (ECOG) PS ≤ 2
* Documented diagnosis of one of the below CD19+ B-cell neoplasms according to WHO classification (Swerdlow et al., 2016) or WHO classification 2008:
1. Diffuse large B-cell lymphoma - de novo or transformed
2. High-grade B-cell lymphoma
3. Primary mediastinal large B-cell lymphoma
4. Follicular lymphoma
5. Mantle cell lymphoma
6. Marginal zone lymphoma (nodal, extranodal, or mucosa-associated)
* Relapsed, progressive, and/or refractory disease after at least 2 lines of therapy.
* For Part B expansion cohorts:
1. Cohort B1: R/R DLBCL that has relapsed after at least 2 prior therapies including a CD20 monoclonal antibody and anthracycline.
2. Cohort B2: R/R FL (grade 1-3a) that has relapsed after at least 2 prior therapies including CD20 monoclonal antibody and an alkylating agent.
3. Cohort B3: Other R/R B-NHL.
* Measurable disease defined as ≥1 measurable nodal lesion (long axis \>1.5 cm and short axis \>1.0 cm) or ≥1 measurable extra-nodal lesion (long axis \>1.0 cm) on computed tomography (CT) scan or magnetic resonance imaging (MRI) AND baseline fluorodeoxyglucose-positron emission tomography (FDG-PET) scan demonstrating positive lesion(s) compatible with CT- or MRI-defined anatomical tumor sites.
* Laboratory parameters including the following:
1. Lymphocyte count \< 5 x 10\^9/L
2. Platelet count ≥ 75 x 10\^9/L
3. Absolute neutrophil count ≥ 1.0 x 10\^9/L; growth factor support allowed in cases of documented bone marrow involvement
4. Hemoglobin ≥ 9 g/dL, with or without transfusion
5. Creatinine clearance ≥ 45 mL/min
6. Total bilirubin ≤ 1.5 × upper limit of normal (ULN), except patients with confirmed Gilbert's Syndrome
7. Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 3.0 × ULN (unless attributed to hepatic involvement by lymphoma)
Exclusion Criteria:
* Primary CNS lymphoma or known CNS involvement by lymphoma at study screening
* Known past or current malignancy other than the inclusion diagnosis
* Known clinically significant cardiac disease
* Significant central nervous system disease
* Prior organ allograft
* Confirmed history or current autoimmune disorder or other disease requiring ongoing immune suppression
* Active Hepatitis C Virus (HCV), Hepatitis B Virus (HBV), or known Human Immunodeficiency Virus (HIV) infection
* Live virus vaccines within 28 days of the first dose of CLN-978, during treatment, and until the end of last dose of CLN-978
* Known active, clinically significant bacterial, viral, fungal, mycobacterial, parasitic, or other infection, including coronavirus disease of 2019 (COVID-19) infection, at the time of enrollment or within 7 days of the first dose of CLN-978.
* Prior treatment with any of the following:
1. Allogeneic HSCT
2. Autologous HSCT within 30 days prior to the first dose of CLN-978
3. Chimeric antigen receptor T cell therapy (CAR-T) within 30 days prior to the first dose of CLN-978
4. Any investigational CD19 x CD3 T cell engager (TCE)
5. Unconjugated CD19 monoclonal antibody ≤ 4 weeks prior to the first dose CLN-978
6. Radio-conjugated or CD19 antibody-drug conjugate ≤ 12 weeks prior to the first dose CLN-978
7. Investigational or standard of care monoclonal antibodies, chemotherapy, or other investigational agent ≤ 4 weeks or 5 half-lives, whichever is shorter, prior to the first dose of CLN-978
8. Radiation therapy (XRT), with the exception of focal treatment for symptom control, ≤ 4 weeks of the first dose of CLN-978
* Woman of child-bearing potential who is pregnant, breast-feeding, or plans to become pregnant
* Male patients who plan to father a child or donate sperm within 120 days of last study drug administration
