Mesothelin-Targeted Immunotoxin LMB-100 in Combination With Tofacitinib in Persons With Previously Treated Pancreatic Adenocarcinoma, Cholangiocarcinoma and Other Mesothelin Expressing Solid Tumors

Background: * Pancreatic cancer is the fourth most common cause of cancer death in the United States, claiming more than 40,000 lives each year. * Incidence nearly equals mortality with just 6% of participants living five years beyond their diagnosis. Most patients are diagnosed at an advanced stage, but even patients with early-stage disease have a long-term survival of less than 20%. * Cholangiocarcinoma is a rare disease and just 3,000 patients are diagnosed with the extrahepatic form yearly. The median overall survival of patients with advanced disease receiving standard of care treatment is less than 1 year. * Expression of mesothelin (MSLN) in pancreatic ductal adenocarcinoma (PDA) has been examined in several published studies and ranges from 86 to 100%. Similar incidence of expression has been observed in extrahepatic cholangiocarcinoma. * In addition to pancreatobiliary tumors, many other solid tumor types also express MSLN such as mesothelioma, colorectal, lung adenocarcinomas, epithelial ovarian, gastric and triple negative breast cancers, as well as some tumors of squamous cell origin. * LMB-100 and a closely related immunotoxin also targeting MSLN have been studied in previous Phase 1 clinical studies for mesothelioma and pancreatic cancer. * Results from these studies showed that almost all patients formed anti-drug-antibodies (ADAs) that neutralized subsequent injection of the product making it ineffective. * Tofacitinib is an oral Janus Kinase-1 and -3 (JAK) inhibitor approved by the FDA for the treatment of rheumatoid arthritis and ulcerative colitis. * Pre-clinical studies have shown that tofacitinib can prevent the formation of ADAs against an immunotoxin closely related to LMB-100 * Co-administration of tofacitinib with immunotoxin increased immunotoxin serum half- life in mice and enhanced anti-tumor efficacy * This clinical trial will investigate whether co-administration of tofacitinib with LMB- 100 can prevent or delay the formation of ADAs and thus allow patients to receive additional effective cycles of LMB-100. Objectives: * The primary objective of the dose escalation phase of this study is to assess the safety and tolerability of LMB-100 given in combination with tofacitinib to patients with pancreatic adenocarcinoma, extrahepatic cholangiocarcinoma and other mesothelin-positive solid tumors * The primary objective of the expansion phase of this study is to determine whether co-administration of tofacitinib delays formation of neutralizing anti-LMB-100 ADAs through cycle 2 of treatment (as measured by LMB-100 serum drug levels) in patients with pancreatobiliary cancers. Eligibility: * Age \>= 18 years * Histologically confirmed solid tumor malignancy for which no curative therapy exists * Participants must have received at least one prior systemic treatment regimen for their disease OR be ineligible to receive available standard treatments for their disease OR refused first-line standard systemic treatments but have been treated with other anti-cancer agents. Design: * This is a Phase I study which will accrue up to 45 subjects total, accounting for screen failure. * Participants will be co-treated for 3 cycles with tofacitinib given orally for the first 10 days of each 21-day cycle, and LMB-100 given on days 4, 6 and 8. * A 3+3 dose escalation schema will be used. Two dose levels are planned. One minus dose level could be utilized if dose de-escalation is necessary. * Following identification of an optimal dose and schedule, an expansion phase of 15 participants will be initiated at the optimal dose for patients with pancreatic adenocarcinoma and extrahepatic cholangiocarcinoma. At least 8 participants in the expansion phase must have pancreatic adenocarcinoma. * Participants on the Dose Escalation and Dose Expansion Arms who appear to be obtaining clinical benefit from LMB-100/tofacitinib after 3 cycles of treatment may elect to receive additional cycles of therapy at the discretion of the principal investigator (PI).