Ipilimumab (Immunotherapy) and MGN1703 (TLR Agonist) in Patients With Advanced Solid Malignancies

Inclusion Criteria: 1. Patients must have a histologically-confirmed metastatic or locally advanced solid tumor that has failed to respond to standard therapy, progressed despite standard therapy, or for which standard therapy does not exist. 2. There is no limit on the number of prior treatment regimens. 3. Patients must be off prior chemotherapy, hormonal therapy, or biological therapy for at least 4 weeks or \>3 half-lives whichever comes first. Patients with prostate cancer may continue to receive LHRH agonist (unless orchiectomy has been performed). 4. ECOG performance status \</= 2 (Karnofsky \>60%). 5. Patients must have adequate organ and marrow function as defined below within 7 days: WBC \>/= 2500/mm\^3. Absolute neutrophil count (ANC) \>/= 1,500/mm\^3. Absolute lymphocyte count (ALC) \>/= 500/mm\^3. Hemoglobin \>/= 9g/dl. Platelets \>/= 75,000/mm\^3. Creatinine \</= 2.0 x ULN or measured CrCl of \>/= 50ml/m\^2/1.73 m\^2. Total bilirubin \</= 2.0 mg/dL (unless previously diagnosed with Gilbert's Syndrome). AST(SGOT)/ALT(SGPT) \</= 3 times the institutional upper limit of normal (patients with liver involvement will be allowed \</= 5.0 X institutional upper normal limit). 6. Patients must have recovered from toxicity related to prior therapy to at least grade 1 (defined by CTCAE 4.0) or baseline level. Chronic stable grade 2 peripheral neuropathy secondary to neurotoxicity from prior therapies may be considered on a case by case basis by the Principal Investigator. 7. As the effect of these drugs on the developing human fetus is not known, women of child-bearing potential and men must agree to use adequate contraception (abstinence; hormonal or barrier method of birth control) for the study and at least 2 months after completion. 8. Female patient of childbearing potential has a negative serum pregnancy test within 7 days of study enrollment. 9. Patients must be willing and able to review, understand, and provide written consent before study enrollment. 10. Measurable disease as defined by irRC or RECIST 1.1 criteria 11. Age \>/= 18 years. Exclusion Criteria: 1. Severe autoimmune disease: Patients with a history of inflammatory bowel disease (including Crohn's disease and ulcerative colitis) and autoimmune disorders such as rheumatoid arthritis, systemic progressive sclerosis \[scleroderma\], Systemic Lupus Erythematosus or autoimmune vasculitis \[e.g., Wegener's Granulomatosis\] are excluded from this study. Patients with history of mild autoimmune disorders - including but not limited to mild psoriasis or Hashimoto's hyperthyroidism may be included at the discretion of the principle investigator. 2. History of acute diverticulitis, intra-abdominal abscess, GI obstruction, abdominal carcinomatosis or other known risk factors for bowel perforation. 3. Any underlying medical or psychiatric condition, which in the opinion of the Investigator, will make the administration of study drug hazardous or obscure the interpretation of AEs: e.g. a condition associated with frequent diarrhea or chronic skin conditions, recent surgery or colonic biopsy from which the patient has not recovered, or partial endocrine organ deficiencies. 4. Current evidence of active and uncontrolled infection, NYHA Class III-IV CHF, documented Child's class B-C cirrhosis, active pancreatitis or uncontrolled medical disease which in the opinion of the investigator could compromise assessment of efficacy. 5. Known human immunodeficiency virus (HIV)-positive and on highly active antiretroviral therapy (HAART), and/or Hepatitis B or C on treatment. Drug interactions between those agents and these experimental agents are wholly unknown (screening not required). 6. Major surgical procedure, open biopsy, or significant traumatic injury within 28 days of day 1 of therapy. 7. Known hypersensitivity to the components of study drugs, its analogs, or drugs of similar chemical or biologic composition. 8. Any non-oncology vaccine therapy used for prevention of infectious diseases (for up to one month prior to or after any dose of ipilimumab). 9. Concomitant therapy with any of the following: IL-2, interferon or other non-study immunotherapy regimens; cytotoxic chemotherapy; immunosuppressive agents; other investigational therapies; or chronic use of systemic corticosteroids (when used in the management of cancers other than intracranial glioblastoma, gliosarcoma or anaplastic astrocytoma, or when used to treat non-cancer-related illnesses). 10. Radiation therapy within 4 weeks of study enrollment (exception is radiotherapy expansion arm which requires radiation treatment within 2 week period). 11. Pregnant and breastfeeding women are excluded from this study. Women of child-bearing potential and men must agree to use contraception prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician. 12. Use of any other concurrent investigational agents or anticancer agents including hormonal therapy, except in the case of prostate cancer patients who are being treated with LHRH agonist at the time of trial entry. 13. Previous exposure to TLR agonist therapy. 14. Known history of plasma cortisol and adrenocorticotropic hormone (ACTH) levels consistent with adrenal failure.