Inclusion Criteria
Must have a histologically or cytologically confirmed advanced solid tumor that is metastatic, unresectable, or recurrent and is refractory to available therapy, or patient has a contraindication to, is intolerant of, or has declined available therapy
Must have adequate coagulation function
Must have adequate hematologic function
Must have adequate renal and hepatic function
Exclusion Criteria
Has received prior therapy with a TLR agonist
Has received anti-cancer chemotherapy (including molecular-targeted drugs), radiotherapy, immunotherapy (e.g., vaccines or cytokines), or investigational agents within the 28 days prior to the first dose of DSP-0509
Receives concurrent systemic (oral or IV) steroid therapy > 10 mg prednisone daily or its equivalent for an underlying condition
Has had major surgery within the 4 weeks before the first dose of DSP-0509
Has CNS metastases (spinal metastases are acceptable); CNS primary tumors (e.g., glioblastoma [GBM])
Has history of seizures other than isolated febrile seizure in childhood; has a history of a cerebrovascular accident or transient ischemic attack less than 6 months ago
Has effusions (pleural, pericardial, or ascites) requiring drainage
Has a motor neuron disease, e.g., Parkinson's disorder, multiple sclerosis
Has retinal detachment, ulcerative keratitis, uveitis, Vogt-Koyanagi-Harada syndrome, choroidal neovascularization, retinopathy/retinitis, thyroid-associated orbitopathy, idiopathic orbital inflammation, diabetic retinopathy, ischemic retinopathy including glaucoma-associated retinopathy, retinal vein thrombosis, or a non-healing ocular or ophthalmic disease (the presence of these conditions would prevent an accurate assessment of the potential ocular and ophthalmic toxicities of DSP-0509)
Has interstitial lung disease or active, non-infectious pneumonitis
Has a history of autoimmune disease active or past including but not limited to inflammatory bowel disease, systemic lupus erythematosus (SLE), ankylosing spondylitis, scleroderma, or multiple sclerosis. Has any active immunologic disorder requiring immunosuppression with steroids or other immunosuppressive agents (e.g., azathioprine, cyclosporine A) with the exception of patients with isolated vitiligo, resolved childhood asthma or atopic dermatitis, controlled hypoadrenalism or hypopituitarism, and euthyroid patients with a history of Grave's disease. Patients with controlled hyperthyroidism must be negative for thyroglobulin, thyroid peroxidase antibodies, and thyroid-stimulating immunoglobulin prior to study drug administration
Has a known hypersensitivity to a component of the protocol therapy, DSP-0509, or another pyrimidine compound
Has a history of another primary cancer within the 5 years prior to enrollment except for the following: non-melanoma skin cancer, cervical carcinoma in situ, superficial bladder cancer, or other non-metastatic carcinoma that has been in complete remission without treatment for more than 5 years
Has abnormal electrocardiograms (ECGs) that are clinically significant, such as QT prolongation (corrected QT interval [QTc] > 470 msec)
In the opinion of the treating Investigator, has any concurrent conditions that could pose an undue medical hazard or interfere with the interpretation of the study results; these conditions include, but are not limited to ongoing or active infection, clinically significant non-healing or healing wounds, concurrent congestive heart failure (New York Heart Association Functional Classification Class II, III or IV), concurrent unstable angina, concurrent cardiac arrhythmia requiring treatment (excluding asymptomatic atrial fibrillation), recent (within the prior 12 months) myocardial infarction, acute coronary syndrome or stroke within the previous 12 months, significant pulmonary disease (shortness of breath at rest or on mild exertion) for example due concurrent severe obstructive pulmonary disease, concurrent hypertension requiring more than 2 medications for adequate control, or diabetes mellitus with more than 2 episodes of ketoacidosis in the prior 12 months
Has the presence of a known active acute or chronic infection including human immunodeficiency virus (HIV) as determined by enzyme-linked immunosorbent assay (ELISA) and confirmed by Western blot; and hepatitis B virus (HBV) and hepatitis C virus (HCV) as determined by hepatitis B surface antigen (HBAg) and hepatitis C serology
Has a cognitive, psychological or psychosocial impediment that would impair the ability of the patient to receive therapy according to the protocol or adversely affect the ability of the patient to comply with the informed consent process, protocol, or protocol-required visits and procedures
Receives concurrent strong inhibitors or inducers of major cytochrome P450 enzymes (CYPs)
Receives concurrent inhibitors of organic anion transporting peptide (OAT) P1B1 and OATP1B3
Is pregnant or breastfeeding

Participants will not be paid for their participation.