Phase 2 Study of Copanlisib in Combination With Nivolumab in Subjects With Relapsed/Refractory Diffuse Large B-Cell Lymphoma and Primary Mediastinal Large B-Cell Lymphoma

• Patients must have a histopathologically confirmed diagnosis of diffuse large B-cell lymphoma (DBLCL) or primary mediastinal large B-cell lymphoma

• Patients must have measurable disease, defined as at least one lesion that is \>= 15 mm (\>= 1.5 cm) in the longest axis on cross-sectional imaging and measurable in two perpendicular dimensions per spiral computed tomography (CT) scan or positron-emission tomography (PET)-CT scan

• Patients must have disease that is recurrent or refractory to standard therapy; patients must have failed front-line therapy and declined or are not candidates for autologous stem cell transplant (ASCT) or have failed prior ASCT

• Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2

• Life expectancy of greater than 12 weeks

• White blood cell (WBC) \>= 2000/mm\^3

• Absolute neutrophil count (ANC) \>= 1000/mm\^3

• Platelet count \>= 100,000/mm\^3

• Hemoglobin \> 9.0 g/dL

• Total bilirubin =\< 1.5 x upper limit of normal (ULN) (except patients with Gilbert syndrome, who can have total bilirubin \< 3.0 mg/dL)

• Aspartate transaminase (AST) =\< 2.5 x ULN

• Serum creatinine =\< 2.0 mg/dL OR calculated creatinine clearance (CrCl) \>= 30 mL/min (if using the Cockcroft-Gault formula)

• Negative urine or serum pregnancy test for females of child bearing potential within 7 days prior to registration

‣ The effects of copanlisib and nivolumab on the developing human fetus are unknown; for this reason, and because the study drugs used in this trial are known to be teratogenic, females of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation and for 5 months after the last dose of study drug; males who are the sexual partners of a female of child-bearing potential must use any contraceptive method with a failure rate of less than 1% per year for the duration of study participation and for a period of 7 months after the last dose of study drug; these periods of required use of contraception have been calculated using the upper limit of the half-life for nivolumab (25 days) and are based on the protocol requirement that females of child-bearing potential use contraception for 5 months and males who are the sexual partners of females of child-bearing potential use contraception for 7 months

⁃ Females must not be breast-feeding for 1 month after last dose

⁃ Females of child bearing potential must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin \[HCG\]) within 24 hours prior to the start of nivolumab

⁃ A female of child-bearing potential is defined as any female who has experienced menarche and who has not undergone surgical sterilization (hysterectomy or bilateral oophorectomy) or who is not postmenopausal; menopause is defined clinically as 12 months of amenorrhea in a female over 45 in the absence of other biological or physiological causes; in addition, females under the age of 55 must have a documented serum follicle stimulating hormone (FSH) level less than 40 mIU/mL

⁃ Females who are not of childbearing potential (i.e., who are postmenopausal or surgically sterile) and azoospermic males do not require contraception

⁃ Should a female of child-bearing potential become pregnant or suspect she is pregnant while she or her partner is participating in this study, she (or the participating partner) should inform the treating physician immediately

• Ability to understand and the willingness to sign a written informed consent document