Study of Carfilzomib With Irinotecan in Irinotecan-Sensitive Malignancies and Small Cell Lung Cancer Patients

Inclusion Criteria: * Patients must have histologically or cytologically-confirmed diagnosis of progressive or recurrent malignancy as follows: * Phase II: extensive stage small cell lung cancer with progression or recurrence after exactly one platinum-containing regimen. Patients who progressed during or within one month of completing platinum-based chemotherapy will be excluded. Patients who received primary curative chemoradiation therapy for limited disease, but who recur within the primary tumor site, previously radiated field or with distant metastases are also allowed to participate. Patients who have clinical evidence of recurrent small cell lung cancer do not require a confirmatory biopsy to be eligible for this trial. Prior irinotecan is not allowed. * Patients must have measurable disease per RECIST criteria 1.1 performed within 28 days prior to enrollment. All other required tests to assess non-measurable disease must be performed within 42 days prior to enrollment. * Patients with known brain metastases are eligible only if he/she has been treated for brain metastasis, are asymptomatic after treatment, have a stable CT or MRI of the brain within 28 days of enrollment and are not receiving corticosteroid therapy to control symptoms from brain metastasis. Only a non-enzyme inducing anticonvulsant (e.g., Keppra) will be permitted for those patients requiring anticonvulsants. (Topical and/or inhaled steroids are allowed.) * Patients may have received previous radiation therapy, but it must have been completed at least 21 days prior to enrollment and the patient should have recovered from all associated toxicities. Measurable or non-measurable disease must be present outside the previous radiation field or a new lesion inside the radiation port must be present. * Patients may have received prior surgery provided that at least 28 days have elapsed since major surgery (thoracic or other major surgeries) and the patient has recovered from all associated toxicities. Patients must have disease outside of the previous surgical resection area or a new lesion must be present. * Patients must have a serum creatinine ≤ the institutional upper limit of normal OR a creatinine clearance ≥ 60 cc/min, measured or calculated (Cockcroft-Gault formula), obtained within 14 days prior to registration. * Patients must have adequate hepatic function as documented by a bilirubin ≤ 2 x the institutional upper limit of normal, an alkaline phosphatase ≤ 2 x the institutional upper limit of normal, and an Serum Glutamate Oxaloacetic Transaminase (SGOT) and Serum Glutamate Pyruvate Transaminase (SGPT) ≤ 2 x the institutional upper limit of normal all obtained within 14 days prior to enrollment. * Patients must have an Absolute Neutrophil Count (ANC) ≥ 1,500/μl and a platelet count ≥ 100,000/μl obtained within 14 days prior to registration. * Patients must be 18 years of age or older. * Patients must have a Zubrod Performance Status as follows: 1. Phase Ib: 0 or 1 2. Phase II: 0, 1 or 2 * Patients must not be pregnant or nursing. Women/men of reproductive potential must have agreed to use an effective contraceptive method (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. * Male subjects must agree to practice contraception. * All patients must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines. Exclusion Criteria: * No prior irinotecan or carfilzomib * Must not have leptomeningeal metastases. * Must be no anticipated need for concurrent radiation therapy during protocol treatment. * Subjects that progressed during or within one month of completion of first-line platinum-based chemotherapy will be excluded. * Patients must not be pregnant or lactating females. * Must have had no major surgery within 28 days prior to enrollment. * Must not have acute active infection requiring treatment (systemic antibiotics, antivirals, or antifungals) within 14 days prior to enrollment. * Must not have any known human immunodeficiency virus infection. * Must not have known active or clinically significant hepatitis A, B or C infection. * Must not have had any unstable angina or myocardial infarction within 4 months prior to enrollment, New York Heart Association (NYHA) Class III or IV heart failure, uncontrolled angina, history of severe coronary artery disease, severe uncontrolled ventricular arrhythmias, sick sinus syndrome, or electrocardiographic evidence of acute ischemia or Grade 3 conduction system abnormalities unless subject has a pacemaker. * Must not have any uncontrolled hypertension or uncontrolled diabetes within 14 days prior to enrollment. * Must not have any evidence of other clinically active cancer and have no history of prior malignancy within the past 3 years with the exception of a) adequately treated basal cell carcinoma, squamous cell skin cancer, or thyroid cancer; b) carcinoma in situ of the cervix or breast; c) prostate cancer of Gleason Grade 6 or less with stable prostate-specific antigen levels; or d) cancer considered cured by surgical resection or unlikely to impact survival during the duration of the study, such as localized transitional cell carcinoma of the bladder or benign tumors of the adrenal glands or pancreas. * Must not have any significant neuropathy (Grades 3-4, or Grade 2 with pain) within 14 days prior to enrollment. * Must not have any known history of allergy to Captisol® (a cyclodextrin derivative used to solubilize carfilzomib). * Must have no contraindication to any of the required concomitant drugs or supportive treatments, including hypersensitivity to all anticoagulation and antiplatelet options, antiviral drugs, or intolerance to hydration due to preexisting pulmonary or cardiac impairment. * Must not have any other clinically significant medical disease or condition that, in the Investigator's opinion, may interfere with protocol adherence or a subject's ability to give informed consent.