Continuous 24h Intravenous Infusion of Mithramycin, an Inhibitor of Cancer Stem Cell Signaling, in People With Primary Thoracic Malignancies or Carcinomas, Sarcomas or Germ Cell Neoplasms With Pleuropulmonary Metastases

* INCLUSION CRITERIA: * Patients with measurable inoperable, histologically confirmed non-small cell lung cancer (NSCLC), small cell lung cancer (SCLC), esophageal carcinomas, thymic neoplasms, germ cell tumors, malignant pleural mesotheliomas or chest wall sarcomas, as well as patients with gastric, colorectal, pancreas or renal cancers, and sarcomas metastatic to thorax. * Histologic confirmation of disease in the Laboratory of Pathology, Center for Cancer Research (CCR), National Cancer Institute (NCI), National Institutes of Health (NIH). * Disease amenable to biopsy via percutaneous approach or other minimally invasive procedures such as thoracoscopy, bronchoscopy, laparoscopy, or gastrointestinal (GI) endoscopy. * Age \>= 18. * Eastern Cooperative Oncology Group (ECOG) status 0-2. * Patients must have had, or refused first-line standard chemotherapy for their inoperable malignancies. * Patients must have had no chemotherapy, biologic therapy, or radiation therapy for their malignancy for at least 30 days prior to treatment. Patients may have received localized radiation therapy to non-target lesions provided that the radiotherapy is completed 14 days prior to commencing therapy, and the patient has recovered from any toxicity. At least 3 half-lives must have elapsed since monoclonal antibody treatment. At least 6 weeks must have elapsed between mitomycin C or nitrosourea treatment. * Patients must have adequate organ and marrow function as defined below: 1. Hematologic and Coagulation Parameters * Peripheral absolute neutrophil count (ANC) greater than or equal to 1500/mm(3) * Platelets greater than or equal to 100,000/ mm(3) (transfusion independent) * Hemoglobin greater than or equal to 8 g/dL (PRBC transfusions permitted) * Prothrombin Time (PT)/partial thromboplastin time (PTT) within normal limits (patient may be eligible for trial if abnormality is deemed clinically insignificant and cleared for protocol therapy by Hematology Consult service) 2. Hepatic Function * Bilirubin (total) \< 1.5 times upper limit of normal (ULN) * Alanine aminotransferase (ALT) Serum glutamic pyruvic transaminase(SGPT) less than or equal to 3.0 times ULN * Albumin \> 2 g/dL 3. Renal Function * Creatinine within normal institutional limits or creatinine clearance greater than or equal to 60 mL/min/1.73 m(2) for patients with creatinine levels above institutional normal. * Normal ionized calcium, magnesium and phosphorus (can be on oral supplementation) * Cardiac Function: Left ventricular ejection fraction (EF) \>40% by echocardiogram, multigated acquisition scan (MUGA), or cardiac magnetic resonance (MR). * Ability of subject to understand, and be willing to sign informed consent. * Female and male patients (and when relevant their partners) must be willing to practice birth control (including abstinence) during and for 2 months after treatment if female of childbearing potential or male having sexual contact with a female of childbearing potential. * Patients must be willing to undergo 2 tumor biopsies. EXCLUSION CRITERIA: * Patients with unfavorable ATP Binding Cassette Subfamily B Member 4 (ABCB11), Ral binding protein (RALBP) or Cytochrome P450 Family 8 Subfamily B Member 1 (CYP8B1) genotypes associated with mithramycin-mediated hepatotoxicity * Clinically significant systemic illness (e.g. serious active infections or significant cardiac, pulmonary, hepatic or other organ dysfunction), that in the judgment of the PI would compromise the patient's ability to tolerate protocol therapy or significantly increase the risk of complications. * Patients with cerebral metastases. * Patients with any of the following pulmonary function abnormalities will be excluded: forced expiratory volume (FEV), \< 30% predicted; diffusing capacity for carbon monoxide (DLCO), \< 30% predicted (post-bronchodilator); Oxygen saturation less than or equal to 92% on room air (per vital sign measurement). Arterial blood gas will be drawn if clinically indicated. * Patients with evidence of active bleeding, intratumoral hemorrhage or history of bleeding diatheses, unless specifically occurring as an isolated incident during reversible chemotherapy-induced thrombocytopenia. * Patients on therapeutic anticoagulation. Note: Prophylactic anticoagulation (i.e. intraluminal heparin) for venous or arterial access devices is allowed. * Patients who are concurrently receiving or requiring any of the following agents, which may increase the risk for mithramycin related toxicities, such as hemorrhage: * Thrombolytic agents * Aspirin or salicylate-containing products, which may increase risk of hemorrhage * Dextran * Dipyridamole * Sulfinpyrazone * Valproic acid * Clopidogrel * Lactating or pregnant females (due to risk to fetus or newborn, and lack of testing for excretion in breast milk). * Patients with history of human immunodeficiency virus (HIV), hepatitis B virus (HBV) or hepatitis C virus (HCV) due to potentially increased risk of mithramycin toxicity in this population. * Hypersensitivity to mithramycin. * Patients who in the opinion of the investigator may not be able to comply with the safety monitoring requirements of the study.