Serial Measurements of Molecular and Architectural Responses to Therapy (SMMART) PRIME Trial

Key Inclusion Criteria:

* Ability to understand and the willingness to sign a written informed consent document
* Participants \>= 21 years old at time of informed consent. Both men and women and members of all races and ethnic groups will be included
* Participants, both men and women, must agree to use an adequate method of contraception prior to study entry, for the duration of study participation, and for 4 months after completion of study
* Women of childbearing potential must have a negative serum or urine pregnancy test within 14 days prior to start of study drug administration
* Patients must have a histologically or cytologically-confirmed metastatic solid tumor or hematological malignancy that has progressed as follows:

  * Patients with a solid tumor must have metastatic disease and have progressed on at least 1 line of established therapy that is known to provide clinical benefit, or for whom no standard curative therapy exists. Participants with newly diagnosed, unresectable, locally-advanced or metastatic pancreatic adenocarcinoma and are beginning first-line treatment with a course of chemotherapy are eligible OR
  * Participants must have a hematological malignancy that is advanced, relapsed, or refractory to at least 1 line of established therapy that is known to provide clinical for the treatment of their disease. Hematological disease included in this study are as follows:

    * Acute myelogenous leukemia (AML), or
    * Myelodysplastic syndrome (MDS), or
    * MDS/myeloproliferative neoplasms (MDS/MPN), or
    * Primary myelofibrosis (PMF)
    * Acute lymphoblastic leukemia (ALL)
    * Chronic myelogenous leukemia (CML)
    * Non-Hodgkin lymphoma (NHL) or Hodgkin's disease (HD)
    * Chronic lymphocytic leukemia (CLL)/small lymphocytic lymphoma (SLL)
    * Multiple myeloma (MM)
* Participants with a metastatic solid tumor or advanced hematological malignancy whom, due to medical issues cannot receive standard therapy shown to prolong survival, will be eligible, if other eligibility criteria are met

  * Patients with a metastatic solid tumor or advanced hematological malignancy that actively refuse chemotherapy that is considered standard treatment for their cancer, despite being informed by the investigator about the treatment options, are eligible for this study on a case-by-case basis (in consultation with the principal investigator \[PI\]). Potential participants actively refusing chemotherapy must have had progression or refractory disease prior to starting study treatment, and their refusal must be documented
* Participants must have measurable disease:

  * Patients with solid tumors must have measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) version (v) 1.1. At least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral computed tomography (CT) scan, per RECIST (v1.1)
  * Note: Participants with lesions on a bone scan that are considered distinctly metastatic will also be included
  * Patients with lymphoma must have at least one non-irradiated tumor mass \> 15 mm (long axis of lymph node) or \> 10 mm (short axis of lymph node or extranodal lesions) on spiral CT-scan
  * Patients with CLL must have presence of radiographically measurable lymphadenopathy (defined as the presence of \>= 1 nodal lesion that measures \>= 2.0 cm in the longest diameter \[LD\] and \>= 1.0 cm in the longest perpendicular diameter \[LPD\] as assessed by CT or magnetic resonance imaging \[MRI\])
  * Patients with MM must have at least one of the following: serum monoclonal component \> 1 g/dL (IgG), or \> 0.5 g/dL (IgA), or Bence-Jones (BJ) proteinuria \> 200 mg/24 hour, or measurable plasmacytoma (not previously irradiated)
* Participants with a hematological malignancy must have their bone marrow biopsy and aspirate reviewed at Oregon Health \& Science University (OHSU)
* Participants with a solid tumor must have lesions meeting the above criteria also and must be amenable to biopsy procedures performed per institutional standards
* Participants must not currently be receiving any other investigational agents
* Participants must have Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 and a physician assessed life expectancy of \>= 6 months
* Absolute neutrophil count (ANC) \>= 1,500/mcL (at time of registration and within 4 weeks prior to initiating on-protocol treatment)

  * Waived for those with hematological malignancy; and may be waived on a case-by-case basis for patient populations recognized to have normal baseline values below this level
* Platelets \>= 100,000/mcL (at time of registration and within 4 weeks prior to initiating on-protocol treatment)

  * Waived for those with hematological malignancy
* Hemoglobin \>= 9 g/dL or \>= 5.6 mmol/L (at time of registration and within 4 weeks prior to initiating on-protocol treatment)

  * Waived for those with hematological malignancy
* Creatinine =\< 1.5 x upper limit of normal (ULN) OR measured or calculated creatinine clearance (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance \[CrCl\]) \>= 60 mL/min/1.73 m\^2 for participants with creatinine levels \> 1 x institutional ULN (at time of registration and within 4 weeks prior to initiating on-protocol treatment)

  * Waived for those with hematological malignancy; and may be waived on a case-by-case basis for patient populations recognized to have normal baseline values below this level
* Total bilirubin =\< 1.5 x ULN OR direct bilirubin =\< ULN for participants with total bilirubin levels \> 1.5 x ULN (at time of registration and within 4 weeks prior to initiating on-protocol treatment)

  * Creatinine clearance should be calculated per institutional standard. For participants with a baseline calculated creatinine clearance below normal institutional laboratory values, a measured baseline creatinine clearance should be determined. Individuals with higher values felt to be consistent with inborn errors of metabolism will be considered on a case-by-case basis
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x ULN (at time of registration and within 4 weeks prior to initiating on-protocol treatment)
* International normalized ratio (INR) or prothrombin time (PT) =\< 1.5 x ULN unless participant is receiving anticoagulant therapy as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants (at time of registration and within 4 weeks prior to initiating on-protocol treatment)
* Activated partial thromboplastin time (aPTT) or PTT =\< 1.5 x ULN unless participant is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants (at time of registration and within 4 weeks prior to initiating on-protocol treatment)
* Body mass index (BMI) \> \> 16.0 and \< 35.0 kg/m\^2 (at time of registration and within 4 weeks prior to initiating on-protocol treatment)

  * Participants with a BMI of \>= 30.0 will use ideal body weight indices in calculating the delivery of agents that are dosed based upon body surface area (i.e., mg agent/meter squared) or weight (i.e., mg agent/kg body weight)
* Any prior therapy, radiotherapy (except palliative radiation therapy of 30 Gy or less), or major surgery must have been completed \>= 4 weeks prior to start of study treatment. All adverse events due to prior therapy must have resolved to a grade 1 or better (except alopecia and lymphopenia for all disease cohorts, and hematologic toxicity for those with a hematological malignancy) by start of treatment. Palliative radiation therapy must have been completed at least 2 weeks prior to start of treatment. The radiotherapy must not be to a lesion that is included as measurable disease
* Additional cancer-specific inclusion criteria must also be met

Key Exclusion Criteria:

* Participants with metastases to the central nervous system that are considered uncontrolled and/or were diagnosed within the past 4 weeks of screening for this study
* Participants cannot have an active malignancy of another cancer. Those with a history of prior malignancy will be considered on a case-by-case basis. Guiding examples for those who can be enrolled include: individuals who have been disease free for \> 5 years; individuals who are considered to have a high likelihood of being cured (e.g., prior history of stage 1 rectal cancer and currently otherwise disease free); adequately treated localized non-melanomatous skin cancer
* Participants cannot be on other forms of anti-cancer therapy at the same time, except as described within this protocol. There must be at least a washout period that accounts for 5 half-lives (or \>= 21 days, whichever is longer) of last therapy

  * Participants with prostate cancer (PCa) will continue treatment with androgen deprivation therapy, either by prior castration or treatment with luteinizing hormone-releasing hormone (LHRH) antagonists or agonists, as is standard practice
  * Participants with breast cancer (BCa) who are HER2 positive may continue to receive anti-HER2 therapy per standard practice guidelines, while participants who are hormone receptor positive may continue to receive hormone therapy per standard practice guidelines
  * Participants with a hematological malignancy may continue to receive hydroxyurea or other hypomethylating agent for two cycles of SMMART-PRIME therapy, as described in this protocol
* Uncontrolled intercurrent illness including, but not limited to, symptomatic congestive heart failure, unstable angina pectoris, serious cardiac arrhythmia, myocardial infarction within 6 months prior to enrollment, New York Heart Association (NYHA) class III or IV heart failure
* Chronic graft versus host disease (GVHD) or on immunosuppressive therapy for the control of GVHD
* Participants with uncontrolled infection will not be enrolled until infection is treated
* Participant is seropositive with human immunodeficiency virus (HIV) or has active infection with hepatitis B virus (HBV) or hepatitis C virus (HCV)

  * HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial
  * For patients with evidence of chronic HBV infection, the HBV viral load must be undetectable on suppressive therapy, if indicated
  * Individuals with a history of HCV infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load
* Participants with medical conditions, inclusive of psychiatric, that in the opinion of the investigators would jeopardize the patient or the study will be excluded
* Participants that are pregnant or breast feeding
* ON-TREATMENT: Individuals that have medical and/or psychiatric conditions that in the opinion of investigators would jeopardize participant safety or study integrity if they were to receive on-study treatment will not proceed further treatment and will be removed from study
* ON-TREATMENT: If performance status is ECOG \> 2
* ON-TREATMENT: History of allergic reaction to a recommended study agent or its excipients
* Additional cancer-specific exclusion criteria requirements