Inclusion Criteria:  Adult 18 to 80 years old at screening  Pathologically confirmed, locally advanced or metastatic unresectable solid tumor, or Hodgkin or Non-Hodgkin lymphoma (including transformed lymphoma) of an acceptable histology:  that is eligible for treatment with a PD-1 or PD-L1 inhibitor, or that is refractory or resistant to standard therapy, or for which standard or curative therapy is not available. Have received ≥ 2 prior systemic anti-cancer therapies (lymphoma subjects only) Protocol-defined measurable disease Available tumor biopsy representative of current disease ECOG performance status grade 0-1 Life expectancy of ≥ 3 months Recovery to Grade ≤ 1 for any non-laboratory toxicity resulting from previous anticancer therapy prior to first dose of ALPN-202 (except alopecia, hearing loss, Grade ≤ 2 neuropathy, or endocrinopathy managed with replacement therapy) Adequate baseline hematologic, renal, and hepatic function  Exclusion Criteria:  Any history of ≥ Grade 3 immune-related adverse event (irAE) Active or prior pneumonitis or interstitial lung disease Presence of any active central nervous system metastases Prior organ allograft or allogeneic hematopoietic stem cell transplantation Any serious or uncontrolled health condition, which, in the opinion of the Investigator, would place the subject at undue risk from the study, impair the ability of the subject to receive protocol specified therapy, or interfere with the interpretation of study results.  Receipt of any protocol-restricted therapy within the timeframes indicated:  PD-L1 inhibitors: 5 half-lives (e.g., atezolizumab, 135 days; avelumab, 31 days; durvalumab, 85 days) PD-1 inhibitors: one scheduled standard dosing interval Other checkpoint inhibitors, including CTLA-4 inhibitors (e.g., ipilimumab, tremelimumab): 4 weeks Chemotherapy, small molecule anticancer agents (e.g., kinase inhibitors), or radiation: 2 weeks Other monoclonal antibodies, antibody-drug conjugates, bispecific antibodies, antibody-like drugs, cytokines, cell therapies, or radioimmunoconjugates: 4 weeks Any active, known, or suspected autoimmune disease Systemic treatment with corticosteroids (> 10 mg/day prednisone) or other immunosuppressive medication Any second malignancy active within the previous 3 years Active infection requiring therapy at the time of the first dose of ALPN-202. Known seropositivity for or active infection by human immunodeficiency virus, hepatitis B or C, or or Severe Acute Respiratory Syndrome Coronavirus 2. Known allergies, hypersensitivity, or intolerance to ALPN-202 or excipients in the drug product formulation. History of Grade 4 infusion-related, anaphylactic or allergic reaction to any previous Fc-based protein therapy.