This study is a Open Label Prospective Dose-Ranging Escalation and Expansion Trial to Evaluate Safety, Tolerability, Pharmacokinetics, Pharmacodynamics, Dosing, and Efficacy of RLS-0071 for the secondary treatment of acute Graft-versus-Host Disease (aGvHD) in hospitalized patients who are steroid-refractory.

Inclusion Criteria:

• Male or female adults or adolescents (>12 years old).
• Hospitalized with steroid-refractory aGvHD (grade II-IV) after allo-HSCT
• Anticipated hospital length-of-stay of at least 1 week from the time of RLS-0071 initiation.
• No plans to add additional GvHD treatment medications or to add, dose-adjust, or discontinue GvHD prophylactic medications during the 7-days of RLS-0071 treatment.
• Neutrophil recovery following the stem-cell transplantation, defined as blood neutrophil count >500/mL for at least 3 consecutive measurements and not supported by growth factor supplementation
• Weight ≥40 kg and ≤ 140 kg at screening.

Exclusion Criteria:

• Has received more than 1 allo-HSCT
• Current, previous, or planned use of any systemic treatment in addition to or other than corticosteroids or ruxolitinib for aGvHD
• Previous failure of ruxolitinib treatment
• Uncontrolled GI infection
• Endoscopic and biopsy testing (if performed) that definitively rules out lower GI aGvHD
• Chronic GvHD
• Participants with evidence of relapsed primary disease, or participants who have been treated for relapse after the allo-HSCT was performed.
• Unresolved toxicity or complications (other than aGvHD) due to the allo-HSCT
• Any corticosteroid therapy for indications other than aGvHD at doses of methylprednisolone or equivalent >1 mg/kg per day within 7 days of enrollment.
• Severe organ dysfunction unrelated to underlying aGvHD
• Known hypersensitivity, allergy, or anaphylactic reaction to polyethylene glycol (PEG)
• Significant liver disease that is unrelated to GvHD
• Severe kidney disease
• Currently breast feeding.
• Known pregnancy, a positive pregnancy test at screening, or lactation for WOCBP.
• Active hepatitis B virus (HBV) or hepatitis C virus infection that requires treatment or human immunodeficiency virus (HIV)-1 or HIV-2.
• Active sepsis