Polarized Dendritic Cell (aDC1) Based Treatment, Interferon Alpha-2, Rintatolimod, and Celecoxib for the Treatment of HLA-A2+ Refractory Melanoma

Inclusion Criteria: * Participant must be HLA-A2+. Retesting is not required for patients who have previous documented positivity * Have IO-refractory melanoma with primary PD-1/PD-L1resistance. Note: Any lines of prior therapies are allowed, but the last line needs to include an anti PD-1 or anti PD-L1 agent. The prior treatments may include any standard and/or experimental therapies * Have \>= 1 tumor site amenable to core needle biopsy that is not the site of disease used to measure antitumor response * Have measurable disease based on RECIST 1.1 criteria present * Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 * Platelets \>= 75,000/microliter * Hemoglobin \>= 9 g/deciliter * Absolute neutrophil count (ANC) \>= 1500/microliter * Creatinine \< 1.5 x institutional upper limit of normal (ULN) OR creatinine clearance \>= 50 mL/min by Cockcroft-Gault formula for subjects with creatinine levels \>= 1.5 x ULN * Total bilirubin not greater than 1.5 x institutional ULN, except for patients with known Gilbert's Syndrome, who are eligible to no more than 2 x institutional ULN * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) no greater than 3 x institutional ULN OR, no greater than 5 x ULN for subjects with liver metastases * Participants of child-bearing potential must agree to use adequate contraceptive methods (e.g., hormonal or barrier method of birth control; abstinence) prior to study entry. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately * Participant must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure * Candidate for continuation/resumption of anti-PD-1/PD-L1 blockade (in parallel to DC vaccine and CKM) Exclusion Criteria: * Is currently being treated with systemic immunosuppressive agents, including steroids: Subjects will be ineligible until 3 weeks after removal from immunosuppressive treatments, except when they are administered as replacement therapy for endocrine dysfunction (and receive no more than 10 mg prednisone or equivalent: inhaled steroids are allowed) * Has had prior anti-cancer therapy within 2 weeks prior to study day 1 or who has not recovered (i.e., no more than grade 1 or at baseline) from adverse events due to a previously administered agent, except for neuropathy (no more than grade 2) or alopecia or vitiligo (any grade) * Has a known additional malignancy that is progressing or requires active treatment * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Treated brain metastases are allowed, if stable for more than 4 weeks (and receive no more than 10 mg prednisone or equivalent: inhaled steroids are allowed). * Has a history of cardiac event(s) (acute coronary syndrome, myocardial infarction, or ischemia (within 3 months of signing consent) or, subject has a New York Heart Association classification of III or IV * Has an active infection requiring systemic therapy * Has known active hepatitis B or hepatitis C infection * Has known immunosuppressive disease (e.g. human immunodeficiency virus \[HIV\], acquired immunodeficiency syndrome \[AIDS\] or other immune depressing disease). Testing is not mandatory * Has known serious hypersensitivity reactions to pegylated (peg)-interferon alpha-2b or interferon alpha-2b * Prior allergic reaction or hypersensitivity to sulfonamides, celecoxib, or nonsteroidal anti-inflammatory drugs (NSAIDs) * Has received a blood transfusion in the two weeks prior to leukapheresis * Women of child bearing potential who are pregnant or nursing * Unwilling or unable to follow protocol requirements * Any condition which in the Investigator's opinion deems the participant an unsuitable candidate or unacceptable risk to receive study drug regimen * Patients who showed initial response to PD-1/PD-L1 blockade and developed secondary resistance