SS1P and Pentostatin Plus Cyclophosphamide for Mesothelioma

* INCLUSION CRITERIA: Mesothelioma Cohorts (Cohorts 1 and 2 Only) * Subjects must have histologically confirmed epithelial or biphasic mesothelioma not amenable to potentially curative surgical resection. However, patients with biphasic tumors that have a less than or equal to 50% sarcomatoid component will be excluded. The diagnosis will be confirmed by the Laboratory of Pathology / Center for Cancer Research (CCR) / National Cancer Institute (NCI). * Patients must have had at least one prior chemotherapy regimen, with the Food and Drug Administration (FDA) approved regimen of a platinum-based therapy in combination with pemetrexed being preferred unless there was a specific contraindication for an individual patient. There is no limit to the number of prior chemotherapy regimens received. * Total Bilirubin less than or equal to 1.5 X institutional upper limit of normal (ULN) INCLUSION CRITERIA: Lung Adenocarcinoma Cohort (Cohort 3) Only * Subjects must have histologically confirmed advanced (Stage IIIB/IV) lung adenocarcinoma. The diagnosis will be confirmed by the Laboratory of Pathology/CCR/NCI. * Patients must have had at least one prior therapy for advanced disease \[platinum containing chemotherapy or one of the approved targeted therapies (an approved estimated glomerular filtration rate (EGFR) tyrosine kinase inhibitor (TKI) for EGFR mutant tumors or crizotinib and ceritinib for ALK translocated tumors)\]. There is no limit to the number of prior chemotherapy regimens received. * Mesothelin expression in at least 5% of cells as assessed in archival tumor tissue samples, determined by the immunohistochemistry (IHC) assay performed at Laboratory of Pathology / CCR / NCI. Archival samples must be available for eligibility. * Total Bilirubin less than or equal to 1.5 X institutional upper limit of normal (ULN) INCLUSION CRITERIA: Pancreatic Cancer Cohort (Cohort 4) Only * Subjects with recurrent, locally advanced unresectable or metastatic adenocarcinoma of the pancreas. The diagnosis will be confirmed by the Laboratory of Pathology/CCR/NCI. * Patients must have had at least one prior chemotherapy for advanced disease. There is no limit to the number of prior chemotherapy regimens received. * Total Bilirubin less than or equal to 2 X institutional upper limit of normal (ULN) INCLUSION CRITERIA: All Subjects * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>20 mm with conventional techniques or as \>10 mm with spiral CT scan. See Section 11 for the evaluation of measurable disease. * Patients must not have had major surgery, radiation therapy, chemotherapy, biologic therapy (including any investigational agents), or hormonal therapy (other than replacement), within 4 weeks prior to entering the study and must have evidence of stable or progressive disease to be eligible. * Age greater than or equal to 18 years. Since the study diseases are extremely rare in children they are excluded from this study. * Performance status (Eastern Cooperative Oncology Group (ECOG)) less than or equal to 1 * Patients must have adequate organ and marrow function (as defined below). * leukocytes less than or equal to 3,000/mm\^3 * absolute neutrophil count less than or equal to 1,500/mm\^3 * hemoglobin less than or equal to 9 g/dL * platelets less than or equal to 90,000/ mm\^3 * total bilirubin See guidelines for individual cohorts in sections 3.1.1.3, 3.1.2.4 and 3.1.3.3 * Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase (SGOT))/alanine aminotransferase (ALT)(serum glutamic-pyruvic transaminase (SGPT)) less than or equal to 3 X institutional upper limit of normal (ULN) (5x if liver function test (LFT) elevations due to liver metastases) * creatinine less than or equal to 1.5 X institutional ULN OR --creatinine clearance greater than or equal to 45 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal, obtained through calculated or measured Creatinine Clearance Patients may be transfused to obtain a hemoglobin of less than or equal to 9 g/Dl. * The effects of SS1(dsFv)PE38, pentostatin, and cyclophosphamide on the developing human fetus are unknown. For this reason, women of child-bearing potential and men must agree to use adequate contraception (barrier method of birth control; abstinence) for the duration of study therapy and for 3 months after the last dose of therapy. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. While hormonal methods of birth control are effective, we ask that female patients who are participating in the study cease hormonal forms of birth control, as these methods of birth control (birth control pills, injections, or implants) may affect the study drug. Patients must be off hormonal forms of birth control for at least 4 weeks prior to initiating the study. * Ability to comply with intravenous administration schedule, and the ability to understand and the willingness to sign a written informed consent document. EXCLUSION CRITERIA: (All Subjects) * Patients with symptomatic brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. However, patients who have had treatment for their brain metastases and whose brain metastatic disease status has remained stable for at least 4-6 weeks without steroids may be enrolled at the discretion of the principal investigator. * Uncontrolled medical illness including, but not limited to, ongoing or uncontrolled, symptomatic congestive heart failure (American Heart Association (AHA) Class II or worse), uncontrolled hypertension, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Human immunodeficiency virus (HIV) positive patients will be excluded due to a theoretical concern that the degree of immune suppression associated with the treatment may result in progression of HIV infection. * Patients with Hepatitis B and C will be excluded. * Serum neutralization antibody assay shows greater than or equal to 75% neutralization of the SS1 (dsFv) PE38 activity at 200 ng/ml. * Patients may not be receiving any other investigational agents. * History of another invasive malignancy in the last two years. Adequately treated noninvasive, non-melanoma skin cancers as well as in situ carcinoma of the cervix will be allowed. * Prior treatment with drugs of the immunotoxin class. * Patients with tumor amenable to potentially curative therapy as assessed by the investigator. * Pregnant women are excluded from this study because SS1(dsFv)PE38, pentostatin, and cyclophosphamide have the potential for teratogenic or abortifacient effects. The agents in the trial may also potentially be secreted in milk and therefore breastfeeding women should be excluded. Because of the potential of teratogenic or abortifacient effects women of childbearing potential and men must agree to use adequate contraception (barrier methods) before, during the study and for a period of 3 months after the last dose of the investigational agent. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to SS1(dsFv)PE38. INCLUSION CRITERIA: WOMEN AND MINORITIES -Both men and women and members of all races and ethnic groups are eligible for this trial. Every effort will be made to recruit women and minorities in this study.