Could an arthritis drug tame a tough transplant complication?

Copied word for word from the study's registry entry, so the wording is the study team's rather than ours.

Inclusion Criteria: Participants must meet the following criteria on screening examination to be eligible to participate in the study: * Participants must be recipients of an allogeneic bone marrow or stem cell transplantation with myeloablative or reduced intensity conditioning regimens. * Participants must be at least 100 days after the transplantation or a donor lymphocyte infusion. * Participants must have cGVHD (as defined by the National Institutes of Health Consensus Development Project on Criteria for Clinical Trials in Chronic Graft-versus-Host Disease) * Participants may have either extensive or limited cGVHD requiring systemic treatment * Participants must have steroid refractory cGVHD, defined as having persistent signs and symptoms of chronic GVHD despite the use of prednisone at ≥ 0. 5 mg/kg/day (or equivalent) for at least 4 weeks in the preceding 12 months. Patients may remain on steroids while enrolled in the study. * No addition or subtraction of other immunosuppressive medications for at least 4 weeks prior to starting treatment. * On stable immunosuppressive regimen for 2 weeks prior to enrollment. Adjustment of immunosuppressive medications to maintain a therapeutic level is permitted. * Age ≥ 18 years at the time of signing the informed consent form. Reproductive Status: Definition of Women of Child-Bearing Potential (WOCBP). WOCBP comprises women who have experienced menarche and who have not undergone successful surgical sterilization (hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or who are not post-menopausal (see definition below). Post-menopause is defined as: * Women who have had amenorrhea for ≥ 12 consecutive months (without another cause) and who have a documented serum follicle-stimulating hormone (FSH) level \> 35 mIU/mL. * Women who have irregular menstrual periods and a documented serum FSH level \> 35 mIU/mL. * Women who are taking hormone replacement therapy (HRT). The following women are WOCBP: * Women using the following methods to prevent pregnancy: Oral contraceptives, other hormonal contraceptives (vaginal products, skin patches, or implanted or injectable products), or mechanical products such as intrauterine devices or barrier methods (diaphragm, condoms, spermicides). * Women who are practicing abstinence. * Women who have a partner who is sterile (eg, due to vasectomy). WOCBP must be using an acceptable method of contraception to avoid pregnancy throughout the study and for up to 10 weeks after the last dose of study drug in such a manner that the risk of pregnancy is minimized. * WOCBP must have a negative serum or urine pregnancy test result (minimum sensitivity 25 IU/L or equivalent units of HCG) within 0 to 48 hours before the first dose of study drug. * Women must not be breast-feeding. * Sexually active fertile men must use effective birth control if their partners are WOCBP. * Life expectancy of greater than \> 3 months. * ECOG performance status ≤ 2 (see Appendix A). * Laboratory test results within these ranges: * Absolute neutrophil count ≥ 1500/mm³ * Serum creatinine ≤ 2.0 mg/dL * Renal function assessed by calculated creatinine clearance ≥ 60ml/min by Cockcroft-Gault formula (see Appendix B: Cockcroft-Gault estimation of CrCl). * Total bilirubin ≤ 1.5 x ULN (unless hepatic dysfunction is caused by cGVHD)AST (SGOT) and ALT (SGPT) ≤ 3 x ULN (unless hepatic dysfunction is caused by cGVHD). * Patients much have a negative PPD skin test and a negative Quantiferon assay. * Must possess the ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Participants who exhibit any of the following conditions at screening will not be eligible for admission into the study. * Any serious medical condition (including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia), laboratory abnormality, or psychiatric illness/ social situation that would prevent the subject from signing the informed consent form or limit compliance with study requirements. * Any condition, including the presence of laboratory abnormalities, which places the subject at unacceptable risk if he/she were to participate in the study or confounds the ability to interpret data from the study. * Use of any other experimental drug or therapy within 28 days of starting treatment with abatacept. * Use of biologic antibody therapy for cGVHD with rituximab, alemtuzumab, or ATG within 6 months of starting treatment with abatacept. * Use of TNF alpha inhibitors within four weeks prior to study entry. * Ongoing prednisone requirement \>1 mg/kg/day (or equivalent) * New immunosuppressive medication or ECP within 28 days of starting treatment with abatacept. * Donor lymphocyte infusion within 100 days prior to enrollment. * Active malignant disease relapse or other active malignancy with the exception of currently treated basal cell, squamous cell carcinoma of the skin, or carcinoma "in situ" of the cervix or breast. * Participants who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier. * Known seropositive for or positive viral load for HIV or positive viral loads for infectious hepatitis, type B (HBV) or C (HCV). * Uncontrolled intercurrent active infection. Controlled infection on long term suppressive or maintenance therapy is permissible. * Use of live vaccines within four weeks of starting abatacept.