This is a multicenter, open label, Phase 1 dose-escalation study of DSP-7888 Dosing Emulsion administered to adult patients with advanced malignancies. Patients will be administered escalating doses of DSP-7888 Dosing Emulsion intradermally or subcutaneously in accordance with the following regimen: once weekly for four weeks during the Induction Phase, once every 7 to 14 days for 6 weeks during the Consolidation Phase, and once every 14 to 28 days until a discontinuation criterion is met during the Maintenance Phase. Once RP2D is determined from either the intradermal or subcutaneous group, an additional 40 patients evaluable for response may be enrolled as an expansion cohort at this dose and route of administration to confirm safety and tolerability. Separate from the dose-ascending cohort and RP2D expansion cohort described previously, and once the intradermal dose-ascending cohort is completed, up to 20 MDS patients who are refractory to treatment with hypomethylating agents (HMAs) will be enrolled into an MDS expansion cohort. Of these 20 MDS patients, one-half will receive DSP-7888 at 10.5 mg according to the modified schedule employed in Phase 1 (every week for 4 weeks, every 2 weeks until Week 24, and then every 4 weeks; [MDS Cohort 1]). The other half of the MDS patients will receive DSP-7888 at 10.5 mg in an alternative dosing schedule where DSP-7888 is administered every 2 weeks until Week 24, after which it will be administered every 4 weeks (MDS Cohort 2).

Inclusion criteria:

1. Signed written informed consent must be obtained and documented according to International Conference on Harmonisation (ICH) and local regulatory requirements
2. Patient has one of the following histologically or cytologically confirmed advanced malignancies: acute myeloid leukemia (AML), myelodysplastic syndrome (MDS), glioblastoma multiforme (GBM), melanoma, non-small cell lung cancer (NSCLC), ovarian cancer, pancreatic cancer, sarcoma, renal cell carcinoma (RCC)
3. Patient must meet at least one of the following criteria: a. Progressed or recurrent despite standard therapy, b. No standard therapy exists for this malignancy, c. Patient is intolerant of standard therapy, d. Patient is not a candidate for standard therapy, e. For AML and MDS patients: patient is not a candidate for allogeneic hematopoietic stem cell transplantation, f, For sarcoma patients: f-1. Patient has disease that is metastatic or unresectable, f-2. Patient with metastatic disease has had at least one prior line of therapy for metastatic disease, f-3. No curative multimodality options exist
4. Patients must be positive for at least one of the following human leukocyte antigens (HLA): a. HLA-A*02:01, b. HLA-A*02:06, c. HLA-A*24:02
5. ≥ 18 years of age
6. For patients with solid tumors, one of the following must apply: a. Patient has measurable disease as defined by the immune-related response criteria (irRC), b. Patient has ovarian cancer and has disease evaluable by CA-125 only
7. For patients with solid tumors, the following criteria apply: a. Hemoglobin ≥ 9.0 g/dl, b. Absolute lymphocyte count ≥ 1.0 x 10^9/L, c. Absolute neutrophil count ≥ 1.5 x 10^9/L, d. Platelets ≥ 100.0 x 10^9/L
8. Patients with MDS must have been diagnosed as MDS by WHO (4th edition) or French-American-British (FAB) classification
9. Patients with MDS must have failed to respond to, or progressed after, adequate treatment with a hypomethylating agent (HMA), or had documented intolerance of an HMA, and must have an International Prognostic Scoring System (IPSS) score ≥ 1.5
10. For patients with AML or MDS, patient must have white blood cell count (WBC) ≤ 50,000/mL. Hydroxyurea is allowed to achieve this change but must be discontinued a minimum of five (5) days prior to baseline evaluation
11. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
12. Male or female patients of child-producing potential must agree to use contraception or avoidance of pregnancy measures during the study and for 180 days after the DSP-7888 Dosing Emulsion dose
13. Females of childbearing potential must have a negative serum pregnancy test
14. Total bilirubin of ≤ 2.0 mg/dL (≤ 3.0 mg/dL for patients with known Gilbert's syndrome)
15. Aspartate Aminotransferase (AST) ≤ 3.0x the upper limit of normal (ULN)
16. Alanine transaminase (ALT) < 3.0x the upper limit of normal (ULN)
17. Creatinine ≤ 2.0x ULN
18. Life expectancy ≥ 3 months
19. For patients with solid tumors, either archival tumor tissue must be available or patient must consent to undergo on-study tumor biopsy before administration of first dose

Exclusion Criteria:

1. Patient has an extensively disseminated primary glioblastoma
2. Patient has acute promyelocytic leukemia (APML)
3. For AML and MDS patients: patients with a dry tap on bone marrow aspiration during screening
4. Patient has symptomatic brain metastases (i.e., metastases that are accompanied by neurological symptoms or that require treatment with corticosteroids)
5. Patient has an infection requiring treatment with systemic antibiotics or antiviral medication or has completed treatment for such an infection within 14 days prior to planned first dose of study drug
6. Patient requires systemic, pharmacologic doses of corticosteroids (equivalent to >30 mg hydrocortisone/day) Note: Replacement doses (equivalent to ≤ 5 mg prednisone/day), and topical, ophthalmic, and inhalation steroids are permitted as needed
7. Patient has a positive test for Hepatitis B surface antigen, Hepatitis C antibody, human immunodeficiency virus HIV-1 or HIV-2 antibody, or has a history of a positive result for hepatitis C virus (HCV) or HIV
8. Patient has received any of the following treatments within the specified timeframes: a. Surgery, radiotherapy, chemotherapy (including molecular-targeted drugs): 4 weeks (28 days), b. Immunosuppressants or cytokine formulations (excluding G-CSF): 4 weeks (28 days), c. Endocrine therapy or immunotherapy (including biological response modifier therapy): 2 weeks (14 days)
9. Patient has an unresolved ≥ Grade 2 adverse event (AE) from a previous antineoplastic treatment, excluding alopecia and phlebitis
10. Patient has had surgery within 4 weeks prior to first dose
11. Woman who is pregnant or lactating or has a positive pregnancy test at screening. If a woman has a positive pregnancy test, further evaluation may be conducted to rule out ongoing pregnancy to allow the patient to be eligible
12. Patient has any concurrent autoimmune disease or has a history of chronic or recurrent autoimmune disease; these include but are not limited to: multiple sclerosis, Grave's disease, vasculitis, systemic lupus erythematosus, rheumatoid arthritis, systemic sclerosis, myasthenia gravis, ankylosing spondylitis, Wegener's granulomatosis, ulcerative colitis, Crohn's disease, psoriasis requiring systemic therapy, pemphigus, temporal arteritis, dermatomyositis, Sjögren's syndrome, Goodpasture's syndrome, interstitial pneumonitis, interstitial nephritis, or Henoch-Schönlein purpura
13. Patient has, in the opinion of the treating investigator, any intercurrent conditions that could pose an undue medical hazard or interfere with the interpretation of the study results; these conditions include, but not limited to: congestive heart failure (New York Heart Association (NYHA) Class III or IV), unstable angina, cardiac arrhythmia requiring treatment, recent (within the prior 6 months) myocardial infarction, acute coronary syndrome or stroke, severe obstructive pulmonary disease, hypertension requiring more than 2 medications for adequate control, or diabetes mellitus with more than 2 episodes of ketoacidosis in the prior 12 months
14. Patient has Common Toxicity Criteria for Adverse Effects (CTCAE) v 4.0 grade ≥ 2 hemorrhage
15. Patient has pleural effusion, ascites, or pericardial fluid requiring drainage Note: Patient who had drain removal ≥ 14 days prior to planned first dose of study drug and has no sign of worsening is eligible
16. Patient has any other medical, psychiatric, or social condition, including substance abuse, that in the opinion of the investigator would preclude compliance with the requirements of this study
17. Patients with two or more active malignancies (synchronous multiple cancers, or metachronous multiple cancers with a disease-free period of ≤ 5 years, with the exception of carcinoma in situ, mucosal carcinoma, or other carcinomas that have been curatively treated with local therapy)
18. Patient has had previous treatment with the study drug or other Wilms' tumor 1 (WT1)-related immune therapy
19. Patient has history of allergy to any oily drug products
20. Patient has a known hypersensitivity to any of the components of the study drug