Glasdegib-Based Treatment Combinations for the Treatment of Patients With Relapsed Acute Myeloid Leukemia Who Have Undergone Hematopoietic Cell Transplantation

Inclusion Criteria:

* MOLECULAR DIAGNOSIS SEGMENT: Documented informed consent of the participant and/or legally authorized representative
* MOLECULAR DIAGNOSIS SEGMENT: Age: \>= 18 years on the day of signing informed consent
* MOLECULAR DIAGNOSIS SEGMENT: Eastern Cooperative Oncology Group (ECOG) =\< 2
* MOLECULAR DIAGNOSIS SEGMENT: Patients with histologically confirmed acute myeloid leukemia (AML), according to World Health Organization (WHO) criteria, with relapsed disease after allogeneic hematopoietic cell transplantation (alloHCT)

  * Patients with non-central nervous system (CNS) extramedullary disease may be included if they also have marrow disease
  * Patients with acute promyelocytic leukemia (APL) will not be eligible
* MOLECULAR DIAGNOSIS SEGMENT: Fully recovered from the acute toxic effects (except alopecia) to =\< grade 1 of prior anti-cancer therapy
* MOLECULAR DIAGNOSIS SEGMENT: Total bilirubin =\< 2 x ULN (unless has Gilbert's disease) (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* MOLECULAR DIAGNOSIS SEGMENT: Aspartate aminotransferase (AST)=\< 2 x ULN (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* MOLECULAR DIAGNOSIS SEGMENT: Alanine aminotransferase (ALT) =\< 2 x ULN (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar) (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* MOLECULAR DIAGNOSIS SEGMENT: Creatinine clearance of \>= 50 mL/min per 24-hour urine test or the Cockcroft-Gault formula (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* MOLECULAR DIAGNOSIS SEGMENT: If not receiving anticoagulants: international normalized ratio (INR) OR prothrombin time (PT) =\< 1.5 x ULN. If on anticoagulant therapy: PT must be within therapeutic range of intended use of anticoagulants (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* MOLECULAR DIAGNOSIS SEGMENT: If not receiving anticoagulants: activated partial thromboplastin Time (aPTT) =\<1.5 x ULN. If on anticoagulant therapy: aPTT must be within therapeutic range of intended use of anticoagulants (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* MOLECULAR DIAGNOSIS SEGMENT: Left ventricular ejection fraction (LVEF) \>= 45% (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)

  * Note: Echocardiogram to be performed within 28 days prior to day 1 of protocol therapy
* MOLECULAR DIAGNOSIS SEGMENT: Corrected QT (QTc) =\< 470 milliseconds (ms) (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)

  * Note: Electrocardiogram (ECG) to be performed within 14 days prior to day 1 of protocol therapy
* MOLECULAR DIAGNOSIS SEGMENT: Women of childbearing potential (WOCBP): Negative urine or serum pregnancy test. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* MOLECULAR DIAGNOSIS SEGMENT: Agreement by females and males of childbearing potential to use an effective method of birth control or abstain from heterosexual activity from 4 weeks prior to first dose of treatment throughout the study treatment period and 1 month (females) or 1 month (males) from the last dose of study drug

  * Childbearing potential is defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only)
* CHAPTER 1: Documented informed consent of the participant and/or legally authorized representative
* CHAPTER 1: Age: \>= 18 years on the day of signing informed consent
* CHAPTER 1: ECOG =\< 2
* CHAPTER 1: Patients with histologically confirmed AML, according to WHO criteria, with relapsed disease after alloHCT

  * Patients with non-central nervous system (CNS) extramedullary disease may be included if they also have marrow disease
  * Patients with acute promyelocytic leukemia (APL) will not be eligible
* CHAPTER 1: Fully recovered from the acute toxic effects (except alopecia) to =\< grade 1 of prior anti-cancer therapy
* CHAPTER 1: White blood cell count less than 25 x 10\^9 /L prior to initiation of venetoclax. Cytoreduction with hydroxyurea prior to treatment and/or up to 1 week after start of this treatment arm may be required (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* CHAPTER 1: Total bilirubin =\< 2 x ULN (unless has Gilbert's disease) (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* CHAPTER 1: AST =\< 2 x ULN (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* CHAPTER 1: ALT =\< 2 x ULN (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* CHAPTER 1: Creatinine clearance of \>= 50 mL/min per 24-hour urine test or the Cockcroft-Gault formula (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* CHAPTER 1: If not receiving anticoagulants: International normalized ratio (INR) OR prothrombin time (PT) =\< 1.5 x ULN. If on anticoagulant therapy: PT must be within therapeutic range of intended use of anticoagulants (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* CHAPTER 1: If not receiving anticoagulants: Activated partial thromboplastin time (aPTT) =\< 1.5 x ULN If on anticoagulant therapy: aPTT must be within therapeutic range of intended use of anticoagulants (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* CHAPTER 1: QTc =\< 470 milliseconds (ms) (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)

  * Note: ECG to be performed within 14 days prior to day 1 of protocol therapy
* CHAPTER 1: Women of childbearing potential (WOCBP): negative urine or serum pregnancy test. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required
* CHAPTER 1: Agreement by females and males of childbearing potential\* to use an effective method of birth control or abstain from heterosexual activity from 4 weeks prior to first dose of treatment throughout the study treatment period and 6 months (females) or 3 months (males) from the last dose of study drug

  * Childbearing potential is defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only)
* CHAPTER 2: Documented informed consent of the participant and/or legally authorized representative
* CHAPTER 2: Age: \>= 18 years on the day of signing informed consent
* CHAPTER 2: ECOG =\< 2
* CHAPTER 2: Patients with histologically confirmed AML, according to WHO criteria, with relapsed disease after alloHCT

  * Patients with non-central nervous system (CNS) extramedullary disease may be included if they also have marrow disease
  * Patients with acute promyelocytic leukemia (APL) will not be eligible
* CHAPTER 2: Patients with a confirmed susceptible FLT3 mutation (m) (internal tandem duplications (ITD), tyrosine kinase domain (TKD) mutations D835 or I836), or AXL variant expression
* CHAPTER 2: Fully recovered from the acute toxic effects (except alopecia) to =\< grade 1 of prior anti-cancer therapy
* CHAPTER 2: Total bilirubin =\< 2 x ULN (unless has Gilbert's disease) (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* CHAPTER 2: AST =\< 2 x ULN (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* CHAPTER 2: ALT =\< 2 x ULN (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* CHAPTER 2: Creatinine clearance of \>= 50 mL/min per 24-hour urine test or the Cockcroft-Gault formula (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* CHAPTER 2: If not receiving anticoagulants: International normalized ratio (INR) OR prothrombin time (PT) =\< 1.5 x ULN. If on anticoagulant therapy: PT must be within therapeutic range of intended use of anticoagulants (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* CHAPTER 2: If not receiving anticoagulants: Activated partial thromboplastin time (aPTT) =\< 1.5 x ULN If on anticoagulant therapy: aPTT must be within therapeutic range of intended use of anticoagulants (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* CHAPTER 2: QTc =\< 470 milliseconds (ms) (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)

  * Note: ECG to be performed within 14 days prior to day 1 of protocol therapy
* CHAPTER 2: Women of childbearing potential (WOCBP): negative urine or serum pregnancy test. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required
* CHAPTER 2: Agreement by females and males of childbearing potential\* to use an effective method of birth control or abstain from heterosexual activity from 4 weeks prior to first dose of treatment throughout the study treatment period and 6 months (females) or 4 months (males) from the last dose of study drug

  * Childbearing potential is defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only)
* CHAPTER 3: Documented informed consent of the participant and/or legally authorized representative
* CHAPTER 3: Age: \>= 18 years on the day of signing informed consent
* CHAPTER 3: ECOG =\< 2
* CHAPTER 3: Patients with histologically confirmed AML, according to WHO criteria, with relapsed disease after alloHCT

  * Patients with non-central nervous system (CNS) extramedullary disease may be included if they also have marrow disease
  * Patients with acute promyelocytic leukemia (APL) will not be eligible
* CHAPTER 3: Patients with a confirmed susceptible BCR-ABL1 gene fusion
* CHAPTER 3: Fully recovered from the acute toxic effects (except alopecia) to =\< grade 1 of prior anti-cancer therapy
* CHAPTER 3: Total bilirubin =\< 2 x ULN (unless has Gilbert's disease) (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* CHAPTER 3: AST =\< 2 x ULN (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* CHAPTER 3: Creatinine clearance of \>= 50 mL/min per 24-hour urine test or the Cockcroft-Gault formula (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* CHAPTER 3: If not receiving anticoagulants: international normalized ratio (INR) OR prothrombin time (PT) =\< 1.5 x ULN. If on anticoagulant therapy: PT must be within therapeutic range of intended use of anticoagulants (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* CHAPTER 3: If not receiving anticoagulants: activated partial thromboplastin Time (aPTT) =\<1.5 x ULN. If on anticoagulant therapy: aPTT must be within therapeutic range of intended use of anticoagulants (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* CHAPTER 3: Left ventricular ejection fraction (LVEF) \>= 45%

  * Note: Echocardiogram to be performed within 60 days prior to day 1 of protocol therapy
* CHAPTER 3: QTc =\< 470 milliseconds (ms) (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)

  * Note: ECG to be performed within 14 days prior to day 1 of protocol therapy
* CHAPTER 3: Women of childbearing potential (WOCBP): Negative urine or serum pregnancy test. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* CHAPTER 3: Agreement by females and males of childbearing potential\* to use an effective method of birth control or abstain from heterosexual activity from 4 weeks prior to first dose of treatment throughout the study treatment period and 1 month (females) and 1 month (males) from the last dose of study drug

  * Childbearing potential is defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only)
* CHAPTER 4: Documented informed consent of the participant and/or legally authorized representative
* CHAPTER 4: Age: \>= 18 years on the day of signing informed consent
* CHAPTER 4: ECOG =\< 2
* CHAPTER 4: Patients with histologically confirmed AML, according to WHO criteria, with relapsed disease after alloHCT

  * Patients with non-central nervous system (CNS) extramedullary disease may be included if they also have marrow disease
  * Patients with acute promyelocytic leukemia (APL) will not be eligible
* CHAPTER 4: Patients with a confirmed susceptible IDH1 mutation (R132)
* CHAPTER 4: Fully recovered from the acute toxic effects (except alopecia) to =\< grade 1 of prior anti-cancer therapy
* CHAPTER 4: Total bilirubin =\< 2 x ULN (unless has Gilbert's disease) (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* CHAPTER 4: AST =\< 2 x ULN (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* CHAPTER 4: ALT =\< 2 x ULN (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* CHAPTER 4: Creatinine clearance of \>= 50 mL/min per 24-hour urine test or the Cockcroft-Gault formula (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated in the study calendar)
* CHAPTER 4: If not receiving anticoagulants: International normalized ratio (INR) OR prothrombin time (PT) =\< 1.5 x ULN. If on anticoagulant therapy: PT must be within therapeutic range of intended use of anticoagulants (to be performed within 28 days