• Maximum Tolerated Dose of nivolumab in combination with Microtransplantation [ Time Frame: 1.5 years ]
  In the dose escalation portion, patients will be sequentially enrolled in 3 cohorts at dose levels in a standard 3+3 design until the maximum tolerated dose (MTD) of nivolumab in combination with microtransplantation is reached. The MTD will be defined as the dose level where at most 1 out of 6 patients experience a dose limiting toxicity (DLT) and will also be the recommended phase 2 dose (RP2D) strategy.
• Incidence of dose limiting toxicity (DLT) [ Time Frame: 4 years ]
  Dose limiting toxicity will be estimated based on the incidence and intensity of drug related adverse events (AEs) due to microtransplantation and/or nivolumab infusion. DLT will be graded according to the NCI CTCAE version 5.0 criteria and GVHD will be graded by consensus criteria (Przepiorka D et al, BMT, 1995).
• Number of subjects experiencing AE [ Time Frame: 4 years ]

• Overall response rate (%) is defined as the number of patients achieving a complete response or partial response as a proportion of total patients evaluable for response. [ Time Frame: 2.5 years ]
• Progression-free Survival (PFS) [ Time Frame: 4 years ]
  progression-free survival (PFS) is defined as the time interval from the time of enrollment on this study to the date of progressive disease (PD) or death, whichever is first reported. Patients are evaluable for PFS if they receive any treatment as part of this study. One- and two-year PFS estimates will also be calculated
• Overall Survival [ Time Frame: 4 years ]
  Overall Survival (OS) is defined as the time interval from the time of enrollment in this study to the date of death from any cause. If the subject is alive or the vital status is unknown, OS will be censored at the date that the subject is last known to be alive, or their last contact date. One- and two-year survival estimates will be generated.

• Drug: Nivolumab
  Nivolumab (1 mg/Kg or 3 mg/kg) every 2 weeks per cohort dose level and schedule
  Other Name: OPDIVO™, BMS-936558, MDX1106, ONO-4538
• Biological: Microtransplantation
  HLA-mismatched peripheral blood stem cells

• Experimental: Cohort 1: Microtransplantation (MST)
  MST:Infusion of granulocyte colony stimulating factor (G-CSF) mobilized HLA-mismatched peripheral blood stem cells (GPBSC)
  Intervention: Biological: Microtransplantation
• Experimental: Cohort 2/2b: MST + Nivolumab

  2: Microtransplantation (Day 0) + nivolumab (3 mg/kg) every 2 weeks (beginning on Day+14)

  2b: Microtransplantation (Day 0) + nivolumab (1 mg/kg) every 2 weeks (beginning on Day+14).

  Interventions:

  • Drug: Nivolumab
  • Biological: Microtransplantation
• Experimental: Cohort 3/3b: MST + Nivolumab

  3: Microtransplantation (Day 0) + nivolumab (3 mg/kg) every 2 weeks (beginning on Day-1).

  3b: Microtransplantation (Day 0) + nivolumab (1 mg/kg) every 2 weeks (beginning on Day-1).

  Interventions:

  • Drug: Nivolumab
  • Biological: Microtransplantation
• Experimental: Cohort 4: Expansion
  Microtransplantation (Day 0) + nivolumab (at RP2D)
  Interventions:

  • Drug: Nivolumab
  • Biological: Microtransplantation

Inclusion Criteria:

1. Patients with relapsed/refractory B cell lymphomas of the following subtypes:

   • Diffuse large B-cell lymphoma (DLBCL)
   • High-grade B-cell lymphoma, with MYC and BCL2 and/or BCL6 translocations (DHL/THL)
   • B-cell lymphoma, unclassifiable, with features intermediate between DLBCL and classical Hodgkin lymphoma (GZL)
   • Primary mediastinal large B-cell lymphoma (PMBCL)
   • Mantle cell lymphoma (MCL)
   • Follicular lymphoma (FL)
   • Marginal zone lymphoma (MZL)
   • Lymphoplasmacytic Lymphoma / Waldenstrom Macroglobulinemia (LPL/WM)
   • Hodgkin lymphoma (HL)
2. Ability to provide written informed consent for the protocol and understand the investigational nature of the study.
3. Willingness and ability to comply with scheduled visits, treatment plans, laboratory tests, and other procedures.
4. Age ≥ 18 years old.
5. Eastern Cooperative Oncology Group performance status of ≤ 2.
6. Evidence of at least one measurable lesion on imaging, defined as nodes/nodal masses > 1.5 cm, extranodal masses >1.0 cm or PET avid lesions consistent with lymphoma.
7. Women of child-bearing potential, defined as all women physiologically capable of becoming pregnant, and men who are sexually active must use effective methods of contraception from the time of enrollment to 1 month after last therapy administered as part of the protocol.
8. Must have biopsy-proven primary refractory disease or relapsed disease after frontline therapy.

9. Adequate organ function parameters:

   1. Renal function: Creatinine clearance ≥ 45ml/min (Cockrauft-Gault Formula)

   2. Liver function:

      • AST/ALT ≤ 3x the institutional ULN.
      • Total bilirubin ≤ 2x the institutional ULN with the exception of patients with Gilbert syndrome; patients with Gilbert syndrome may be included if their total bilirubin is ≤ 3.0x ULN and direct bilirubin is ≤ 2x ULN
   3. Pulmonary function: PFTs with DLCO ≥ 40%.
   4. Cardiac function: Must have LVEF ≥ 40% confirmed by echocardiogram or MUGA scan.

   5. Bone marrow reserve without transfusion defined as:

      • Absolute neutrophil count (ANC) ≥ 1,000/mm3
      • Platelets ≥ 50,000/mm3
10. Subjects must have a potential 3-5/6 HLA-matched (A, B, DRB1) related haploidentical donor (either a first or second- degree relative) that will be evaluated for eligibility to provide hematopoietic cells for infusion.

Exclusion Criteria:

1. Prior Treatments:

   1. Prior treatment with allogeneic HSCT.
   2. Treatment with CAR-T cells within 6 months of study enrollment.
   3. Treatment with an immune checkpoint inhibitor within 3 months of study enrollment.
   4. Prior grade 3 or higher toxicities with immune checkpoint inhibitor use, excluding lymphopenia, asymptomatic amylase or lipase elevation or laboratory abnormalities that correct to grade 1 within 72 hours.
   5. Chemotherapy, radiation or surgical resection of malignancy within 2 weeks prior to the start of lymphodepleting chemotherapy (washout period).
2. Active, uncontrolled serious infection or medical or psychiatric illness, that in the investigator's opinion is likely to interfere with participation in this clinical trial.
3. Known active CNS involvement by malignancy.
4. History of seizure disorder, cerebrovascular ischemia/hemorrhage, dementia, cerebellar disease, or any autoimmune disease with CNS involvement.
5. Active replication of hepatitis B or active hepatitis C (HCV RNA positive). Those with prior disease who are PCR negative at enrollment and meet liver function eligibility criterion are eligible.
6. Known HIV positive patients.
7. Patients with unstable angina and/or myocardial infarction within 6 months prior to screening.
8. Cardiac arrhythmia not controlled with medical management, evidence of pericardial effusion on imaging that is compromising function.
9. History of a second malignancy requiring treatment at any time within the 3 years prior to study enrollment. The following are allowed within 3 years of study enrollment if subject has received definitive local therapy (i.e., surgical excision, external beam radiation, or other local therapy with curative intent): non-melanoma skin cancers, organ-confined localized prostate cancer treated with curative intent, or carcinoma in situ.
10. Active autoimmune disease, history of primary immunodeficiency, or any syndrome that requires systemic corticosteroids or immunosuppressive medications (excluding Hashimoto's thyroiditis, vitiligo, or DM type I).
11. History of solid organ transplantation.
12. Pregnant or lactating women.
13. Prisoners or those compulsorily detained.