The study will be conducted in two phases. The phase I portion will employ a 3+3 dose-escalation design to define the maximum tolerated dose (MTD) of abatacept added to PTCy and bortezomib following HSCT. The phase II portion will consist of two single-arm, open-label, optimal 2-stage Simon design studies conducted in two separate strata for HLA-matched and HLA-mismatched donor transplants.

The study will be conducted in two phases. The phase I portion will employ a 3+3 dose-escalation design to define the maximum tolerated dose (MTD) of abatacept added to PTCy and bortezomib following HSCT. The phase II portion will consist of two single-arm, open-label, optimal 2-stage Simon design studies conducted in two separate strata for HLA-matched and HLA-mismatched donor transplants. Adult patients with hematological malignancies undergoing allogeneic HSCT from an HLA-matched sibling or ≥7 out of 8 allele level HLA-matched unrelated donor are eligible for the study if they meet the standard criteria defined in our institutional standard operation procedures (SOPs), meet all inclusion criteria, and do not satisfy any exclusion criteria. Subjects will receive a standard of care conditioning regimen followed by peripheral blood hematopoietic stem cells. Subjects with unrelated donors will also receive rabbit anti-thymocyte globulin (rATG). Subjects will receive investigational PTCy, investigational bortezomib, and investigational abatacept as GvHD prophylaxis. The phase II portion dose of abatacept will be the MTD as determined in the phase I portion of the study. In the phase II portion, subjects will be stratified based on whether they receive a matched sibling or matched unrelated (matched) donor transplant and ≥7 out of 8, allele level matched (mismatched) unrelated donor transplant

Inclusion Criteria:

• Age ≥18 years
• Karnofsky score ≥70%
• No evidence of progressive bacterial, viral, or fungal infection
• Creatinine clearance >50 mL/min/1.72m2
• ALT and AST <3 x the upper limit of normal
• Total bilirubin <2 x the upper limit of normal (except for Gilbert's syndrome)
• ALP ≤250 IU/L
• LVEF >45%
• Adjusted DLCO >50%
• Negative HIV serology
• Negative pregnancy test: Confirmation per negative serum β-hCG
• Willing to comply with all study procedures and be available for the duration of the study.

Exclusion Criteria:

• Pregnant or nursing females or women of reproductive capability who are unwilling to completely abstain from heterosexual sex or practice effective methods of contraception from start of conditioning through 90 days after the last dose of study drug. A woman of reproductive capability is one who has not undergone a hysterectomy (removal of the womb), has not had both ovaries removed, or has not been post-menopausal (stopped menstrual periods) for more than 24 consecutive months.
• Male subjects who refuse to practice effective barrier contraception from the start of conditioning through a minimum of 90 days after the last dose of study drug, or completely abstain from heterosexual intercourse. This must be done even if they are surgically sterilized.
• Inability to provide informed consent.
• Patient had myocardial infarction within 6 months prior to enrollment or has NYHA Class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities. Prior to study entry, any ECG abnormality at screening must be documented by the investigator as not medically relevant.
• Known allergies to any of the components of the investigational treatment regimen.
• Serious medical or psychiatric illness is likely to interfere with participation in this clinical study.
• Diagnosed or treated for another malignancy within 3 years of enrollment, with the exception of complete resection of basal cell carcinoma or squamous cell carcinoma, an in-situ malignancy, or low-risk prostate cancer after curative therapy.
• Participation in clinical trials with other investigational agents not included in this trial, within 14 days of the start of this trial and throughout the duration of this trial.
• Prisoners
• Pregnant women