This is a single arm, open label, phase II clinical trial. Adult patients with hematological malignancies undergoing allogeneic HSCT from first- or second-degree haploidentical 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. Patients will receive non-myeloablative, reduced-intensity or myeloablative conditioning regimen followed by peripheral blood hematopoietic stem cells. Patients will receive dosed reduced cyclophosphamide, abatacept, and short-duration tacrolimus for GvHD prophylaxis.

Inclusion Criteria:

• Age ≥ 18 years
• Karnofsky score ≥ 70%
• No evidence of progressive bacterial, viral, or fungal infection
• Creatinine clearance > 50 mL/min/1.72m2
• Total bilirubin, Alanine Aminotransferase and Aspartate Aminotransferase < 2 x the upper limit of normal (except for diagnosed Gilbert's syndrome)
• Alkaline phosphatase ≤ 250 IU/L
• Left Ventricular Ejection Fraction (LVEF) > 45%
• Adjusted Carbon Monoxide Diffusing Capacity (DLCO) > 60%
• Negative HIV serology
• Negative pregnancy test: confirmation per negative serum β-human chorionic gonadotropin (β-hCG) for women of childbearing age and potential.

Exclusion Criteria:

• Donors are excluded in case of donor-specific HLA antibodies or positive cross-match.
• Pregnant or nursing females or women of child bearing age or potential, who are unwilling to completely abstain from heterosexual sex or practice 2 effective methods of contraception from the first dose of conditioning regimen through day +180. 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 months in a row.
• Male subjects who refuse to practice effective barrier contraception during the entire study treatment period and 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 (i.e., post-vasectomy).
• Inability to provide informed consent.
• Patient had myocardial infarction within 6 months prior to enrollment or has New York Heart Association (NYHA) Class III or IV heart failure (see Appendix E), 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 likely to interfere with participation in this clinical study.
• 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

Only available to study team members.