A Study of Vedolizumab With Tofacitinib in Adults With Ulcerative Colitis (UC)

Inclusion Criteria: 1. Has a confirmed diagnosis of UC established at least 3 months prior to screening, by clinical and endoscopic evidence and corroborated by a histopathology report. 2. Has moderately to severely active UC as determined by a complete Mayo score \[including physician's global assessment (PGA)\] of 6 to 12 with a rectal bleeding subscore ≥1 and a centrally assessed endoscopic subscore ≥2 at screening. 3. Has evidence of UC extending proximally to the rectum \[≥15 centimeter (cm) of involved colon\]. 4. Participants with extensive colitis or pancolitis of \>8 years duration or left sided colitis \>12 years duration must have documented evidence that a surveillance colonoscopy was performed within 12 months of the initial screening visit. 5. Participants with a family history of colorectal cancer, personal history of increased colorectal cancer risk, age \>50 years, or other known risk factors must be up to date on colorectal cancer surveillance. 6. Has demonstrated an inadequate response to, loss of response to, or intolerance to at least 1, but no more than 2 TNFα antagonists. Participants without prior failure or intolerance to biologics are not eligible. Participants who discontinued TNFα antagonist therapy for reasons other than failure or intolerance (eg, pregnancy) may be eligible after discussion with the medical monitor. Note: After the interim analysis, participants with inadequate response, loss of response, or intolerance to conventional UC therapy without prior exposure to biologics may be enrolled if deemed appropriate. Participants who discontinued biologics for reasons other than failure or intolerance (eg, pregnancy) may be eligible after discussion with the Medical Monitor. 7. If using corticosteroids must be on a stable dose of oral corticosteroids up to a maximum of 40 mg daily of prednisone or 9 mg daily of budesonide, or equivalent for at least 2 weeks prior to screening endoscopy and must be willing to follow a mandatory taper of corticosteroids from enrollment. Exclusion Criteria: Gastrointestinal Exclusion criteria: 1. Has any of the following UC-related complications: 1. Acute severe UC. 2. The participant has had extensive colonic resection, subtotal or total colectomy. 3. The participant has clinical evidence of abdominal abscess or toxic megacolon. 4. The participant has an ileostomy, colostomy, or known fixed symptomatic stenosis of the intestine. 5. Short bowel syndrome. 2. Has Crohn's colitis, indeterminate colitis, ischemic colitis, nonsteroidal anti-inflammatory drug (NSAID) induced colitis, idiopathic colitis (i.e, colitis not consistent with UC), radiation colitis, microscopic colitis, colonic mucosal dysplasia, or untreated bile acid malabsorption. Participants with a history of colonic mucosal dysplasia are also excluded. 3. Has uncontrolled primary sclerosing cholangitis. Infectious Disease Exclusion Criteria: 1. Has any evidence of an active systemic infection during screening. Participants with nonsystemic infections (eg, active fungal infection of nail beds) may be eligible, if in the opinion of the investigator, inclusion of the participant will not interfere with the collection or interpretation of study results and poses no risk to the participant. 2. Has active or latent tuberculosis (TB), regardless of treatment history, as evidenced by any of the following: 1. History of TB. 2. A diagnostic TB test performed during screening that is positive, as defined by: i. A positive QuantiFERON test or 2 successive indeterminate QuantiFERON tests or ii. A tuberculin skin test reaction ≥10 mm (≥5 mm in subjects receiving the equivalent of \>15 mg daily prednisone). 3. A positive test for hepatitis B virus (HBV). 4. A positive test for hepatitis C virus (HCV). 5. Evidence of, or treatment for, Clostridium difficile infection or other intestinal pathogen within 28 days prior to first dose of study treatment. Participants who test positive for C. difficile or other intestinal pathogens at screening and receive treatment may be enrolled or rescreened (if required) following confirmation of infection resolution. 6. Evidence of active Cytomegalovirus (CMV) infection at screening. Medication exclusion criteria: 1. Has received immunomodulators (eg, 6-mercaptopurine, azathioprine, and methotrexate) within 4 weeks prior to first dose or immunosuppressants (eg, cyclosporine, tacrolimus) within 8 weeks prior to first dose. 2. Any medicinal product, herbal medication, or natural health product which might interfere with cytochrome P450 genotype 3A4 (CYP3A4) within 2 weeks prior to enrollment, except for any CYP3A4 modulator used to treat a C. difficile or an intestinal pathogen infection at screening. 3. Has received any of the following medical therapies for UC: 1. IV antibiotics within 8 weeks prior to enrollment. 2. Any rectal therapy for treatment of UC within 2 weeks prior to screening endoscopy. 3. Chronic NSAID use defined as daily use for \>2 consecutive weeks (Note: occasional use \[\<2 consecutive weeks\] of NSAIDs and acetaminophen \[\<100 mg daily\] for headache, arthritis, myalgias, or menstrual cramps and chronic low dose aspirin use \[81-162.5 mg daily\] for cardiovascular prophylaxis are permitted). 4. Has received a live virus or live bacterial vaccine within 4 weeks prior to enrollment or planned vaccination during the study and for 12 weeks after last dose. General Exclusion Criteria: 1. Has any of the following cardiovascular or thrombotic conditions: 1. Recent (within past 6 months) cerebrovascular accident, myocardial infarction, or coronary stenting. 2. Recent (within past 6 months) moderate to severe congestive heart failure (New York Heart Association class III or IV). 3. Prior history of thrombotic events, including deep vein thrombosis and pulmonary embolism. 4. Known inherited conditions that predispose to hypercoagulability. 2. History of lymphoproliferative disease, including lymphoma, or signs and symptoms suggestive of possible lymphoproliferative disease, such as lymphadenopathy and/or splenomegaly. 3. A surgical procedure requiring general anesthesia within 3 months prior to screening or is planning to undergo major surgery during the study period. 4. Any investigational procedure ≤4 weeks prior to screening that, in the investigator's opinion, may interfere with interpretation of study results.