Inclusion Criteria:

1. Adult participants ≥18 years of age on the day of signing the informed consent form.
2. Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 to 2.
3. Histologically confirmed PTCL-NOS, FHTCLs or sALCL per The International Consensus Classification of Mature Lymphoid Neoplasms.
4. Progressed on, be refractory to, relapsed, or intolerant to standard therapy for their cancer. At least 1 but not more than 3 prior systemic therapies.
5. Fluorodeoxyglucose-avid disease by positron emission tomography and measurable disease of at least 1.5 cm by computed tomography, as assessed by the site radiologist.
6. Life expectancy \>12 weeks.
7. Adequate organ function as determined by:

* Absolute neutrophil count ≥ 1.0×10\^9/L (1000/mm3) (without receiving granulocyte-colony stimulating factor)
* Platelet count ≥ 100×10\^9/L (without transfusion)
* Hemoglobin ≥ 9.0 g/dL, without packed red blood cell transfusion within the last 1 week of starting study drug
* Prothrombin time international normalized ratio and partial thromboplastin time ≤1.5 × upper limit of normal (ULN), unless participant is receiving anticoagulant therapy and prothrombin time or activated partial thromboplastin time is within therapeutic range of intended use of anticoagulants
* Calculated creatinine clearance (CrCl) according to Cockcroft-Gault formula and based on ideal body weight or 24-hour urine CrCl ≥ 50 mL/minute
* Total bilirubin ≤ 1.5 × ULN or direct bilirubin ≤ ULN for participants with total bilirubin levels \> 1.5 × ULN. For participants with Gilbert's disease: ≤ 3.0 mg/dL or discussion with the Medical Monitor
* Aspartate aminotransferase and alanine transaminase ≤ 2.5 × ULN (≤ 5 × ULN for participants with liver metastases)
* Serum albumin \> 2.5 g/dL
* Serum calcium \< 12 mg/dL or corrected serum calcium \< ULN
8. Must have recovered from all AEs due to previous therapies to Grade ≤ 1 or baseline except for the following:

* Grade ≤ 2 neuropathy
* Alopecia and non-acute toxicities
* If major received major surgery, then must have recovered adequately per the investigator from the toxicity and/or complications from the intervention prior to starting study treatment
9. Female participants of childbearing potential who are sexually active with a non-sterilized male partner must agree to use at least 1 highly effective method of contraception from the time of screening and must agree to continue using such precautions for 120 days after the last dose of study drug for participants who receive soquelitinib, or 6 months after the last dose for participants who receive either belinostat or pralatrexate.
10. Non-sterilized males who are sexually active with a female partner of childbearing potential must use a condom plus spermicide from Day 1 through 120 days after the last dose of study drug.

Exclusion Criteria:

1. Participants who have T-cell lymphoma with active central nervous system involvement.
2. Any significant medical condition, laboratory abnormality, or psychiatric illness that would prevent the participant from participating in the study.
3. History of primary immunodeficiency or sold organ transplantation.
4. History of opportunistic infection within 30days of screening requiring active systemic treatment or active infection requiring IV therapy.
5. Any active infection requiring IV therapy.
6. History of invasive prior malignancy that required systemic therapy within last 3 years.
7. Any condition that confounds the ability to interpret data from the study.
8. Known to be positive for HIV, or positive test for chronic hepatitis B virus (HBV) infection (defined as positive hepatitis B surface antigen \[HBsAg\]) or positive test for hepatitis C antibody.
9. Monoclonal antibody therapy for cancer, radiotherapy, or chemotherapy within 3 weeks and targeted therapy within 2 weeks prior to the first dose of study treatment.
10. Prior administration of an ITK inhibitor.
11. Participants who need immediate cytoreductive therapy.
12. Participants requiring the concomitant use of strong inhibitors or inducers of CYP3A or who have received these within 5 half-lives or 14 days prior to the start of study treatment.
13. History of allogeneic hematopoietic stem cell transplantation.
14. Candidate for hematopoietic stem cell transplantation at screening.
15. History of progressive disease within 6 months of autologous hematopoietic stem cell transplantation.
16. Concurrent enrollment in another clinical study
17. Females who are pregnant, lactating, or intend to become pregnant during their participation in the study, starting with the screening visit through 6 months after the last dose of study treatment.
18. Participants who cannot ingest medications orally or who have malabsorption.