• Pathologically-confirmed diagnosis of ALK+ ALCL by WHO/ICC, classification procedures in use at the time of diagnosis. Note that ALK+ ALCL by definition expresses ALK, which is readily detectable on standard IHC. Confirmation through molecular sequencing of the specific ALK translocation and fusion partner is not necessary for enrollment.

• Relapsed or refractory disease after at least one line of prior systemic therapy.

‣ NOTE: Prior systemic therapy must have included at least one cytotoxic chemotherapy agent.

⁃ NOTE: Prior treatment with an ALK inhibitor is allowed.

⁃ NOTE: Patients being treated with an ALK inhibitor immediately prior to enrollment are eligible. This includes patients on an ALK inhibitor who are in clinical remission at the time of enrollment, as long as the patient is not immediately planned for allogeneic transplant.

⁃ NOTE: If the last therapy was an ALK inhibitor, the patient must not have stopped the ALK inhibitor and maintained clinical remission (no relapse) with no intervening therapy for ≥ six months.

⁃ NOTE: Prior progression on ALK inhibitor is not specifically exclusionary though should be reviewed with the MSK Principal Investigator.

• Age ≥ 18 years at the time of enrollment

• ECOG performance status ≤ 2 at the time of enrollment.

• Laboratory criteria:

‣ Absolute neutrophil count ≥ 1.0 K/mcL or ≥ 0.5 K/mcL if due to lymphoma (NOTE: growth factor is allowed).

⁃ Platelet count ≥ 75 K/uL.

⁃ Calculated creatinine clearance ≥ 60 mL/min by Cockcroft-Gault.

⁃ Total bilirubin ≤ 2x upper limit of normal (ULN) or ≤ 3x ULN if due to hepatobiliary involvement with lymphoma, or ≤ 3x ULN if history of Gilbert's disease.

⁃ Aspartate (AST) and alanine (ALT) aminotransferase ≤ 3 x ULN or ≤ 5x ULN if due to hepatobiliary involvement with lymphoma.

⁃ NOTE: Patients with AST and/or ALT \> 3x ULN and total bilirubin \> 2x ULN must be reviewed with the MSK Principal Investigator to determine eligibility.

⁃ NOTE: Patients must meet laboratory criteria prior to initiation of the alectinib lead-in cycle and prior to initiation of combination therapy with duvelisib

• Able to swallow pills.

• Able to take prophylactic medications against Pneumocystis jirovecii pneumonia (PJP)

• Women of reproductive potential must have a negative serum or urine β human chorionic gonadotropin (β-HCG) pregnancy test within 14 days before initiating therapy.

• Females of childbearing age must be on effective contraception per institutional standards during the treatment period and for 5 weeks after the last dose of the study drugs.

• Males must consistently use an effective contraception method per institutional standards during the treatment period and for 3 months following the last dose of the study drugs.