A Dose-Finding Study of Vedolizumab for Treatment of Steroid-Refractory Acute Intestinal Graft-Versus-Host Disease (GvHD) in Participants Who Have Undergone Allogeneic Hematopoietic Stem Cell Transplantation (Allo-HSCT)

Inclusion Criteria

• Recipient of 1 allogeneic hematopoietic stem cell transplantation (allo-HSCT) but not more than 1 allo-HSCT.
• Has primary steroid-refractory graft-versus-host disease (GvHD). Steroid-refractory disease is defined as worsening or no improvement in 5 to 7 days of treatment with methylprednisolone 2 milligram per kilogram (mg/kg) or equivalent or lack of a CR after 14 days of primary treatment with methylprednisolone 2 mg/kg or equivalent. Note that participants who develop intestinal GvHD while receiving systemic therapy for other GvHD are still eligible after 5 to 7 days, even if the intestinal GvHD has not been present for the entire duration. Participants who may have received an increase in their steroid dose treatment (example, increased methylprednisolone from 1 mg/kg to 2 mg/kg) before enrollment will be eligible, provided the participant has met the definition of steroid refractory above. Participants who develop toxicity on corticosteroids or who are otherwise medically unable to be dosed to this level, will also be eligible.
• Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 3.
• Evidence of myeloid engraftment defined by absolute neutrophil count greater than or equal to (>=) 0.5*109/liter (L) on 3 consecutive days.

Exclusion Criteria

• Presence of chronic GvHD at Screening (including acute-chronic overlap syndrome).
• Relapse of underlying malignant disease after allo-HSCT.
• Hyperacute GvHD defined as onset of GvHD within the first 15 days following hematopoietic stem cell infusion.
• Received systemic agents other than corticosteroids for treatment of acute GvHD. GvHD prophylaxis agents (example, calcineurin inhibitors) may be continued.
• Life expectancy of <3 weeks.