Ganetespib and Ziv-Aflibercept in Refractory Gastrointestinal Carcinomas, Non-Squamous Non-Small Cell Lung Carcinomas, Urothelial Carcinomas, and Sarcomas

* INCLUSION CRITERIA: Patients must have histologically confirmed recurrent or metastatic gastrointestinal carcinomas, non-squamous non-small cell lung carcinomas, urothelial carcinomas, and sarcomas with disease progression after at least one line of standard therapy. Disease should have progressed following all treatments known to prolong survival, unless a given treatment is contraindicated. * Patients with colorectal carcinoma must have progressed through at least two lines of standard chemotherapy in the metastatic setting. * Patients with non-small cell lung cancer with known sensitizing epidermal growth factor receptor (EGFR) mutation and/or anaplastic lymphoma receptor tyrosine kinase (ALK) rearrangement should have received prior erlotinib and/or crizotinib, respectively. * Patients with urothelial carcinoma will have progressed on prior platinum-based therapy or for which platinum-based therapy is contraindicated. * Patients enrolled on the expansion phase of the protocol must demonstrate EGFR expression by immunohistochemistry on archival tumor samples prior to undergoing (89) Zr-panitumumab positron emission tomography (PET)/computed tomography (CT) scans. Age greater than or equal to 18 years of age. Eastern Cooperative Oncology Group (ECOG) performance status \< 2. Life expectancy \> 3 months. Patients must have normal organ and marrow function as defined below: * absolute neutrophil count greater than or equal to 1,500/mcL * platelets greater than or equal to 100,000/mcL * total bilirubin less than or equal to 1.5 times institutional upper limit of normal * Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase SGOT)/alanine aminotransferase (ALT)(serum glutamic pyruvic transaminase SGPT) less than or equal to 3 times institutional upper limit of normal * creatinine less than or equal to 1.2 times institutional upper limit of normal OR * creatinine clearance greater than or equal to 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * urine protein/creatinine \< 1 mg/mg * International Normalized Ratio (INR) \< 1.5 Cardiac function within institutional normal limits on echocardiogram. Patients must have blood pressure no greater than 140 mmHg (systolic blood pressure) and 90 mmHg (diastolic blood pressure) for eligibility. Initiation or adjustment of antihypertensive medications is permitted prior to study entry provided that the average of three blood pressure measurements at enrollment visit is less than 140/90 mmHg. The effects of ganetespib on the developing human fetus are unknown. For this reason and because anti-angiogenic agents similar to ziv-aflibercept are known to be teratogenic, women of child-bearing potential and men must agree to use two forms of contraception (hormonal or barrier method of birth control; abstinence; sterilization) prior to study entry, for the duration of study participation, and for 3 months after completing study treatment. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use two forms of contraception prior to the study, for the duration of study participation, and for 3 months after completion of administration of both ganetespib and ziv-aflibercept. Ability to understand and the willingness to sign a written informed consent document. During the escalation phase of the protocol, patients may have evaluable or measurable disease. During the expansion phase of the protocol, patients must have 1) measurable disease, 2) disease amenable to biopsy and 3) willingness to undergo pre- and post-treatment biopsies. EXCLUSION CRITERIA: Patients who have had chemotherapy or radiotherapy within 3 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 3 weeks earlier. Patients who are receiving any other investigational agents. Patients with known active brain metastases or carcinomatous meningitis are excluded from this clinical trial. Patients whose brain metastatic disease status has remained stable for greater than or equal to 4 weeks following treatment of brain metastases are eligible to participate at the discretion of the principal investigator. Uncontrolled intercurrent illness including, but not limited to, ongoing or active untreated infection, or psychiatric illness/social situations that would limit compliance with study requirements. Patients with known serious cardiac illness or medical conditions, including but not limited to: * Clinically unstable cardiac disease, including unstable atrial fibrillation, symptomatic bradycardia, unstable congestive heart failure, unstable angina or history of myocardial infarct within 6 months prior to enrollment, or indwelling temporary pacemaker * Ventricular tachycardia or a supraventricular tachycardia that requires treatment with antiarrhythmic agents * Second- or third-degree atrioventricular block unless treated with a permanent pacemaker * Complete left bundle branch block * History of long Q wave, T wave (QT) syndrome or a family member with this condition No major surgery within 4 weeks prior to enrollment or history of gastrointestinal bleeding within 3 months prior to enrollment. No signs or symptoms of active bleeding or nonhealing ulcer will be permitted at study entry. Patients with central pulmonary tumors with evidence of bronchial invasion, or presenting with hemoptysis will be excluded. Corrected QT interval (QTc) \> 470 msec on electrocardiogram (by Bazett's; average of triplicate recordings at the discretion of the principal investigator (PI) will exclude patients from entry on study. Medications that are known to cause QTc interval prolongation are prohibited for patients entering on trial. Patients for whom a given medication that may cause QTc interval prolongation cannot be discontinued, may be eligible at the discretion of the study PI, provided QTc interval criteria is met at enrollment. A comprehensive list of agents with the potential to cause QTc prolongation can be found in Appendix C and at http://crediblemeds.org. Pregnant women and women who are breastfeeding are excluded from this study because the effects of the study drugs on the developing fetus are unknown. Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with ganetespib and zivaflibercept. In addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated. Substrates of cytochrome P450 3A4 (CYP3A4) or cytochrome P450 2C19 (CYP2C19): * Preliminary results of a clinical drug-drug interaction study, examining the effect of ganetespib on the pharmacokinetics of the CYP2C19-sensitive probe omeprazole, show a modest (20%) increase in omeprazole exposure when coadministered with ganetespib. * In vitro data implies expectation of greater interaction with CYP2C19 substrates than with CYP3A4 substrates. * Caution is advised when sensitive narrow therapeutic range CYP3A4 or CYP2C19 substrates are concomitantly administered. Inhibitors of P-Glycoprotein Efflux Transporters: Concomitant medications that are strong inhibitors of P-glycoprotein efflux transporters should be used with caution during the study; examples of these medications include: * ritonavir, * cyclosporine, * verapamil, * erythromycin, * ketoconazole, * itraconazole, * quinidine, and * elacridar. Concurrent anticoagulation will be permitted providing the patient is receiving a stable dose of anticoagulants before study entry. Patients receiving anticoagulants will be eligible for this trial. Evidence of clinically significant bleeding diathesis or underlying coagulopathy (e.g., INR \> 1.5 without vitamin K antagonist therapy) will not be permitted.