Inclusion Criteria:

        1. Diagnosis of the following, as per Regimen Cohort:

        1A. Regimen A: FT500 Monotherapy (Dose Escalation and Expansion): An advanced solid tumor
        malignancy, including lymphoma, in a subject who has failed or refused available
        FDA-approved therapies and is now a candidate for salvage therapy.

        1B. Regimen B: FT500 + ICI (Dose Escalation): An advanced solid tumor malignancy, including
        lymphomas, that has progressed on treatment with at least one ICI (ie, nivolumab,
        pembrolizumab or atezolizumab), in a subject who has also failed or refused other available
        approved therapies and is now a candidate for salvage therapy.

        1C. Regimen B: FT500 + ICI (Dose Expansion): An advanced solid tumor malignancy, including
        lymphomas, in a subject who is currently receiving nivolumab, pembrolizumab or atezolizumab
        per USPI, with disease progression on the ICI.

        2. Provision of signed and dated ICF.

        3. Presence of measurable disease by iRECIST or RECIL criteria, assessed before the start
        of lympho-conditioning and within 28 days prior to Day 1.

        4. Stated willingness to comply with study procedures and duration. 5. Provision of signed
        and dated ICF to agree to participate, at time of withdrawal or completion of this study,
        in Fate Therapeutics' long-term, non-interventional, observation study, FT-003.

        Exclusion Criteria:

        All Subjects:

          1. Females of reproductive potential who are pregnant or lactating, and males or females
             not willing to use a highly effective form of contraception from Screening through the
             end of the study.

          2. ECOG performance status ≥ 2.

          3. Evidence of insufficient organ function as determined by any one of the following:

               1. Neutrophils <1000/µL or platelets <75,000/µL.

               2. Estimated creatinine clearance <50 mL/minute (Cockcroft-gault).

               3. Total bilirubin >2 x upper limit normal (ULN) with the exception of subjects with
                  Gilbert's Syndrome or known liver metastases.

               4. Aspartate aminotransferase (AST) >3 x ULN, or alanine aminotransferase (ALT) >3 x
                  ULN. For subjects with known liver metastases, AST or ALT >5 x ULN.

               5. Oxygen saturation <90% on room air; pulmonary function tests (PFTs) required if
                  symptomatic or prior known impairment - subject will be excluded if diffusing
                  capacity of the lungs for carbon monoxide (DLCO) or forced expiratory volume 1
                  (FEV1) is <50% of predicted for height and age.

               6. Left ventricular ejection fraction (LVEF) <40% (eg by echocardiogram (ECHO) or
                  multi-gated acquisition (MUGA) scan).

          4. Receipt of any biological therapy, chemotherapy, or radiation (except palliative
             radiation) within 2 weeks prior to Day 1. Subjects in Regimen B currently taking an
             ICI must interrupt ICI dosing at least 2 weeks prior to Day 1.

          5. CNS metastases that have not been treated; or treated CNS metastases that have not
             been stable for at least 6 months.

          6. Clinically significant cardiovascular disease, including stroke or myocardial
             infarction within 6 months prior to first study medication; or the presence of
             unstable angina or congestive heart failure of New York Heart Association grade 2 or
             higher.

          7. Currently receiving or likely to require systemic immunosuppressive therapy (eg,
             prednisone >5 mg daily) for any reason from Day -7 to Day 29.

          8. Uncontrolled infections.

          9. Known allergy to the following FT500 components: Albumin (Human) or DMSO.

         10. Presence of any medical or social issues that are likely to interfere with study
             conduct, or may cause increased risk to subject.

             Additional Exclusion Criteria for Regimen B: FT500 + ICI:

         11. Subjects who experienced an ICI-related adverse reaction that resulted in
             discontinuation of the ICI.

         12. Presence or history of autoimmune disease (eg, lupus erythematosus, rheumatoid
             arthritis, Addison's disease, autoimmune disease associated with lymphoma, Crohn's
             disease, ulcerative colitis), except for subjects with isolated vitiligo, atopic
             dermatitis, controlled hypoadrenalism or hypopituitarism, and controlled thyroid
             disease.

         13. Subjects who have received an allograft organ transplant.