Inclusion Criteria:

• Subject has provided informed consent prior to initiation of any study specific activities/procedures.
• Subject is an adult ≥ 18 years old at the time of signing the informed consent.
• Subject is a recipient of an allogeneic HSCT.
• Subject has moderate to severe steroid-refractory cGVHD
• Subject has received no more than 3 previous treatments for cGVHD
• Subject may be receiving corticosteroid therapy provided that the dose is ≤ 1 mg/kg/day of systemic prednisone or equivalent and has been stable for at least 2 weeks prior to first dose of AMG 592.
• Subject may be receiving other non-corticosteroid immunosuppressive therapies provided that the immunosuppressant dose is stable for at least 2 weeks prior to first dose of AMG 592. Adjustments to dose of calcineurin inhibitor or sirolimus are allowed only to maintain drug levels within therapeutic range.
• Subject has a Karnofsky performance status score ≥ 50%.
• Subject has an estimated life expectancy of > 3 months.
• Subject must have adequate hepatic function
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Exclusion Criteria:

• Subject is concurrently receiving treatment with calcineurin-inhibitor plus sirolimus (either agent alone is acceptable).
• Subject has received ibrutinib, imatinib, bortezomib, entospletinib, ruxolitinib or other JAK inhibitor, or treatment with any investigational drug or device within 4 weeks prior to starting AMG 592.
• Subject has received treatment with T-cell depleting, B-cell depleting or IL-2 signaling targeted medication 
• Subject has received treatment with T-regulatory cell expanding therapies
• Subject has received a donor lymphocyte infusion within 12 weeks prior to starting dose of AMG 592.
• Subject with active morphologic relapse/progression of hematologic malignancy post transplantation. Persistent CLL early after transplantation that subsequently entered remission will not be excluded.
• Subject has a history of malignancy, other than the indication for hematopoietic cell transplantation
• Subject has a history of thrombotic microangiopathy, hemolytic-uremic syndrome or thrombotic thrombocytopenic purpura.
• Subject has an active infection requiring treatment with IV antibiotics or has been hospitalized for treatment of an active infection in the 4 weeks prior to starting dose of AMG 592.
• Active tuberculosis.
• Hepatitis B
• Subject has positive test results for Human Immunodeficiency Virus (HIV) or known to be HIV-positive.
• Phase 1b subject cannot be a current smoker, nor have used any nicotine or tobacco containing products within the last 6 months prior to screening. 
• Phase 1b subject is unable to avoid alcohol during the 4-week DLT evaluation period or tobacco consumption for the duration of the study.
• Subject has known sensitivity to AMG 592 or its excipients to be administered during dosing.
• History or evidence of any other clinically significant disorder, condition, or disease that, in the opinion of the investigator or Amgen physician, if consulted, would pose a risk to subject safety or interfere with the study evaluation, procedures, or completion.
• Females of child-bearing potential with a positive pregnancy test (assessed by a serum pregnancy test at screening and a urine pregnancy test at baseline).
• Females of childbearing potential who are unwilling to use 1 highly effective method of contraception during treatment and for an additional 6 weeks after receiving the last dose of AMG 592.
• Subject has previously entered this study.