• Complete response (CR) [ Time Frame: Up to 36 months ]
  Rate is defined as the percentage of patients who have a best response of CR. CR rate will be analyzed by cohort.
• Duration of response (DOR) [ Time Frame: Up to 36 months ]
  DOR is defined as the time from date of first observed response (CR or PR) to date of PD or death, whichever occurs first. Patients who do not progress or die will be censored on the date of last evaluable tumor assessment. DOR will be analyzed by cohort.
• Progression-free survival (PFS) [ Time Frame: Up to 36 months ]
  PFS is defined as the time from start date of study drug therapy to date of disease progression or death, whichever occurs first. Patients who do not progress or die will be censored on the date of last evaluable tumor assessment. PFS will be analyzed by cohort.
• Overall survival (OS) [ Time Frame: Up to 36 months ]
  OS is defined as the time from start date of study drug therapy to date of death. Patients who do not die will be censored on the date of last contact. OS will be analyzed by cohort.

• Peripheral T-Cell Lymphoma (PTCL NOS)
• Nodal Lymphomas of T Follicular Helper (TFH)
• Follicular T-cell Lymphoma (FTCL)
• AITL
• ALCL
• HSTCL
• EATL I,II
• MEITL, EATL Type II
• Nasal Lymphoma

• Experimental: Cohort A
  Cerdulatinib dosing of patients with Peripherial T-Cell Lymphoma (PTCL) not otherwise specified (NOS); Cerdulatinib 30 mg orally (PO) twice daily (BID) (60 mg daily total)
  Intervention: Drug: Cerdulatinib
• Experimental: Cohort B
  Cerdulatinb dosing of patients with nodal lymphomas of T follicular helper (TFH) phenotype origin, including angioimmunoblastic T cell lymphoma (AITL), follicular T-cell lymphoma (FTCL), and nodal PTCL with TFH phenotype; Cerdulatinib 30 mg orally (PO) twice daily (BID) (60 mg daily total)
  Intervention: Drug: Cerdulatinib
• Experimental: Cohort C
  Cerdulatinb dosing of patients with Anaplastic large cell lymphoma (ALCL) (anaplastic lymphoma kinase positive [ALK+] and negative [ALK-]); Cerdulatinib 30 mg orally (PO) twice daily (BID) (60 mg daily total)
  Intervention: Drug: Cerdulatinib
• Experimental: Cohort D
  Other rare types of extranodal non-cutaneous aggressive PTCL, including hepatosplenic T-cell lymphoma (HSTCL), enteropathy-associated T-cell lymphoma (EATL type I), monomorphic epitheliotropic intestinal T-cell lymphoma (MEITL, EATL type II), and extranodal NK/T-cell lymphoma (nasal type); Cerdulatinib 30 mg orally (PO) twice daily (BID) (60 mg daily total)
  Intervention: Drug: Cerdulatinib

Inclusion Criteria:

1. Ability to give informed consent.
2. A histologically confirmed diagnosis, per the WHO 2016 classification [45], of any PTCL subtype listed for study. Patients may be entered on the basis of local pathology. Local pathology slides must be available for central pathology review.
3. Prior therapy consisting of at least one systemic regimen that involved at least two cycles of treatment.
4. In patients with ALCL, prior treatment with brentuximab vendotin unless, in the judgment of the Investigator, such treatment was otherwise contraindicated.

5. Relapsed/refractory disease after prior therapy:

   • Refractory is defined as progression during treatment or recurrence/progression of disease within ≤ 6 months of completing a treatment regimen that resulted in either SD, a PR, or a CR.
   • Relapse is defined as progression or recurrence of disease after a prior documented response (CR or PR) and > 6 months since last treatment.
6. Age ≥ 18 years.
7. A life expectancy of > 3 months.
8. An Eastern Cooperative Oncology Group (ECOG) performance status of ≤ 2.

9. Adequate bone marrow reserve, defined as an ANC ≥ 1,000/µL and a platelet count ≥ 75,000/µL. The ANC must be without growth factor support for 7 days, and the platelet count must be without transfusion support within 7 days of study drug initiation. Patients with evidence of marrow involvement must have a platelet count ≥ 50,000/μL.

   NOTE: There are no limits on ANC or platelet count for patients with HSTCL as long as cytopenia, if present, is secondary to disease.

10. Adequate renal function, defined as a creatinine clearance of ≥ 30 mL/min calculated using the Cockcroft-Gault equation or based on a 24-hour urine specimen.
11. Adequate hepatic function, defined as: i) a serum bilirubin level ≤ 1.5 × ULN; and ii) serum AST/ALT levels ≤ 2.5 × the ULN for the reference lab. A serum bilirubin level ≤ 2.5 mg/dL is permissible if it is clearly due to Gilbert's syndrome. In patients with lymphoma and documented hepatic involvement, adequate hepatic function is defined as: i) total bilirubin level ≤ 2 × ULN; and ii) AST/ALT levels ≤ 3 × ULN.
12. Measurable disease for a given tumor type, defined as the presence of ≥ 1 lesion measurable per RECIL criteria (≥ 15 mm) as assessed by CT or, in patients with nodal or mass lesions, by CT/PET.
13. Female patients of childbearing potential and male patients must agree to abstain from sexual intercourse or to use an effective method of contraception during the study, for 90 days after the last dose of study drug. Examples of effective methods of contraception include oral contraceptives or double barrier methods such as a condom plus spermicide or a condom plus a diaphragm.

Exclusion Criteria:

1. A diagnosis of any one of the following PTCL subtypes: (i) primary cutaneous T-cell lymphoma, including primary cutaneous ALCL and primary cutaneous gamma-delta lymphoma; (ii) mycosis fungoides, including that with large-cell transformation; (iii) Sézary syndrome; and (iv) leukemic forms of PTCL (e.g., adult T cell leukemia/lymphoma, T cell prolymphocytic leukemia, T-cell large granular lymphocyte leukemia, aggressive NK leukemia).
2. Allogeneic or autologous stem cell transplantation within 90 days of study drug initiation or active immunosuppressive therapy for graft-versus-host disease (GVHD) or GVHD prophylaxis within 8 weeks of study drug initiation.
3. Prior cancer therapy with an SYK or JAK inhibitor.
4. The need for chronic treatment with a strong inhibitor, sensitive substrate, or inducer of CYP3A4.
5. Known active lymphoma involvement of the central nervous system.
6. Persistent unresolved toxicity associated with prior treatment that is of Grade ≥ 2 severity (per v5.0 of the National Cancer Institute [NCI] Common Terminology Criteria for Adverse Events [CTCAE]) and is also clinically significant in the judgement of the Investigator. Exceptions are alopecia, erectile impotence, hot flashes, diminished libido, and neuropathy.
7. Other treatment for the PTCL subtype within 3 weeks of study drug initiation.
8. Known infection with HIV, hepatitis B virus (HBV), or hepatitis C virus (HCV) or known HBV or HCV carrier status.
9. Active infection requiring systemic treatment, defined as the need for intravenous antimicrobial, antifungal, or antiviral agents.

10. Clinically significant cardiac disease, defined by any of the following:

    1. A history of clinically significant cardiac disease or congestive heart failure (New York Heart Association Class II). Patients must not have unstable angina (anginal symptoms at rest) or new-onset angina within the last 90 days or myocardial infarction (MI) within the past 6 months.
    2. Clinically significant cardiac arrhythmias, defined as requiring anti-arrhythmic therapy (excluding beta blockers or digoxin). Patients with controlled atrial fibrillation are not excluded.
    3. Congenital long QT syndrome or concomitant medications known to prolong the QT interval except those required for infections that carry a low risk of QTc prolongation.
    4. A Fridericia-corrected QT interval of ≥ 450 msec (males) or ≥ 470 msec (females) at screening.
11. Difficulty swallowing or malabsorption syndrome.
12. Known history of acute pancreatitis within the last 30 days or a known history of chronic pancreatitis.
13. Major surgery within 28 days of study drug initiation.
14. A history of another malignancy within the 2-year period prior to study drug initiation unless the malignancy was treated with curative intent and the likelihood of its relapse is small (< 5% in 2 years in the judgement of the Investigator). Patients with a history of basal cell carcinoma, squamous cell carcinoma of the skin, or carcinoma in situ of the cervix may be enrolled. Patients receiving adjuvant hormonal therapy for breast or prostate cancer are eligible as long as there is no detectable disease at study entry.
15. Chronic systemic steroid treatment at doses greater than the equivalent of prednisone at 20 mg/day, with the exception of intermittent use for the treatment of emesis.
16. Women who are breast-feeding, pregnant, or intend to become pregnant while on study.
17. Known hypersensitivity to any of the components of cerdulatinib.
18. Participation in any other therapeutic clinical study (observational or registry trials are allowed, as is long-term follow-up from other studies for survival).
19. Presence of any other medical, psychological, familial, sociological, or geographic condition potentially hampering compliance with the protocol or that, in the judgment of the Investigator, would interfere with the study endpoints or the patient's ability to participate in the study.