Inclusion Criteria:

        A. Signed Informed Consent B. Ability to comply with the protocol C. Age ≥18 years D.
        Histologically or cytologically documented, locally advanced or metastatic (i.e., Stage
        IIIB not eligible for definitive chemoradiotherapy, Stage IV, or recurrent) NSCLC (per the
        American Joint Committee /AJCC staging system) E. Measurable disease, as defined by RECIST
        v1.1. Previously irradiated lesions can be counted as target lesions if clearly progressing
        after radiation.

        F. Chemotherapy naive and treated patients will be eligible, with no limit on number of
        prior therapies. Patients with NSCLC known to harbor an ALK rearrangement, or EGFR mutation
        known to be sensitive to FDA approved tyrosine kinase inhibitors (TKI), are only eligible
        after experiencing disease progression (during or after treatment) or intolerance to an FDA
        approved EGFR TKI or ALK TKI, respectively.

        G. Positive NY-ESO-1 expression by RT-PCR and/or IHC will be required for entry, as
        determined by analysis at the trial central laboratory.

        H. At least one tumor amenable to excisional, core or forceps (transbronchial) biopsy.
        Patients must be willing to undergo tumor biopsies before starting therapy and after the
        3rd CDX-1401 injection. Additionally, the first 12 patients enrolled must consent to a
        third tumor biopsy to be performed after the 3rd MPDL3280A infusion.

        I. ECOG performance status of 0 to 2 J. For female patients of childbearing potential and
        male patients with partners of childbearing potential, agreement (by patient and/or
        partner) to use a highly effective form(s) of contraception (i.e., one that results in a
        low failure rate [<1% per year] when used consistently and correctly) and to continue its
        use for 6 months after the last dose of trial therapy. Highly effective contraception is
        one with a failure rate of <0.1%. Birth control pills on their own do not achieve that
        rate.

        K. Adequate hematologic and end-organ function, defined by the following laboratory results
        obtained within 14 days prior to the first study treatment:

          -  ANC ≥1500 cells/μL (without granulocyte colony-stimulating factor support within 2
             weeks prior to Cycle 1, Day 1)

          -  Platelet count ≥100,000/μL (without transfusion within 2 weeks prior to Cycle 1, Day
             1)

          -  Hemoglobin ≥9.0 g/dL (Patients may be transfused to meet this criterion)

          -  AST, ALT, and ALP ≤2.5 xULN, with the following exceptions: Patients with documented
             liver metastases: AST and/or ALT≤5 x ULN; Patients with documented liver or bone
             metastases: ALP ≤5 x ULN

          -  Serum bilirubin ≤1.5 xULN (Patients with known Gilbert disease who have serum
             bilirubin level ≤3 xULN may be enrolled)

          -  INR and aPTT≤1.5 x ULN (This applies only to patients who are not receiving
             therapeutic anticoagulation; patients receiving therapeutic anticoagulation should be
             on a stable dose)

          -  Serum creatinine ≤1.5 xULN or creatinine clearance ≥50 mL/min

        Exclusion Criteria:

        A. Has an active autoimmune disease requiring systemic treatment within the past 3 months
        or a documented history of clinically severe autoimmune disease, or a syndrome that
        requires systemic steroids or immunosuppressive agents. Subjects with vitiligo or resolved
        childhood asthma/atopy would be an exception to this rule. Subjects who require
        intermittent use of inhaled steroids or local steroid injections would not be excluded from
        the study. Subjects with hypothyroidism stable on hormone replacement, or psoriasis not
        requiring systemic therapy (within the past 3 years) will not be excluded from the study.

        B. Generalized dermatologic conditions (such as allergic reactions, infection, edema, or
        scarring) that will not allow for study drug administration at a site of normal skin or
        evaluation of localized adverse events.

        C. Symptomatic or untreated CNS metastases. Patients with a history of treated asymptomatic
        CNS metastases are eligible, provided they meet all of the following criteria: No evidence
        of interim progression between the completion of CNS-directed therapy and the start of
        trial therapy. No ongoing requirement for dexamethasone as therapy for CNS disease;
        anticonvulsants at a stable dose are allowed. Completed stereotactic radiation at least 1
        week prior to Cycle 1, Day 1 or whole-brain radiation at least 2 weeks prior to Cycle 1,
        Day 1 D. Treatment with systemic immunosuppressive medications (including but not limited
        to, prednisone at doses > 10 mg (or equivalent dose of other corticosteroids),
        cyclophosphamide, tacrolimus, sirolimus, azathioprine, methotrexate, thalidomide, and
        antitumor necrosis factor [anti-TNF] agents) within 2 weeks prior to CDX-1401
        administration (Inhaled or topically applied steroids, and acute and chronic standard-dose
        NSAIDs are permitted. Replacement steroids are also permitted).

        E. Any approved anti-cancer therapy, including chemotherapy, or hormonal therapy within 3
        weeks prior to initiation of study treatment; the following exceptions are allowed:

          -  Hormone-replacement therapy or oral contraceptives

          -  TKIs approved for treatment of NSCLC discontinued > 7 days prior to Cycle 1, Day 1.
             The baseline scan must be obtained after discontinuation of prior TKIs.

        F. Treatment with any other investigational agent or participation in another clinical
        trial with therapeutic intent within 28 days prior to enrollment; the following exceptions
        are allowed:

        - Unapproved/ experimental TKIs discontinued 14 days prior to Cycle 1, Day 1 G. Known
        infection with HIV, HBV or HCV. Patients with prior exposure to hepatitis, but no evidence
        of active or chronic infection, may be eligible.

        H. Active systemic infection requiring systemic antibiotic treatment within 72 hours prior
        to first dose of study treatment I. Uncontrolled intercurrent illness including, but not
        limited to, symptomatic congestive heart failure, unstable angina pectoris, or psychiatric
        illness/social situations that would limit compliance with study requirements J. Women who
        are pregnant or lactating. K. Any underlying medical condition that in the Principal
        Investigator's opinion will make the administration of study drug hazardous to the patient
        or would obscure the interpretation of adverse events.

        L. Previous administration of vaccine therapy targeting NY-ESO-1 M. Prior treatment with
        immune checkpoint blockade therapies, including anti-CTLA4, anti-PD-1, and anti-PD-L1
        therapeutic antibodies