Inclusion Criteria:

* PRE-REGISTRATION: Age ≥ 18 years
* PRE-REGISTRATION: Not eligible for or have failed therapies with established benefits, at the discretion of the treating physician
* PRE-REGISTRATION: Patients must meet one of the following criteria:

* Relapsed/refractory patients with Erdheim-Chester disease, Langerhans histiocytosis, histiocytic sarcoma, or other malignant histiocytosis without activating alterations in v-Raf murine sarcoma viral oncogene homolog B (BRAF) or Mitogen-activated protein kinase kinase (MAP2K) oncogenes who have progressed after first line of therapy.

* Note: Relapsed is defined as a relapse that occurred after having a response to the last therapy at any point during the treatment. Refractory is no response (stable disease or progressive disease while on therapy) to a given treatment at least after 1 month of being on the given treatment.
* Newly diagnosed patients with Rosai-Dorfman disease without activating alterations in MAP2K oncogenes.
* Relapsed/refractory patients with Rosai-Dorfman disease and an activating mitogen-activated protein kinase (MAPK) pathway alteration who have failed prior treatment with cobimetinib.
* Relapsed/refractory patients with Erdheim-Chester disease or Langerhans histiocytosis who have received vemurafenib for BRAF V600E mutated disease or cobimetinib for disease with activating MAP2K alterations.
* Patients with Erdheim-Chester disease, Rosai-Dorfman disease, Langerhans histiocytosis, histiocytic sarcoma, or another malignant histiocytosis who cannot tolerate or have a contraindication to BRAF or MEK inhibitors or those who cannot have reliable access to these inhibitors due to financial restraints or geographic location or initiation of BRAF or mitogen-activated protein kinase kinase (MEK) inhibitors is futile based on the genomic alterations or the discretion of treating physician.
* Relapsed/refractory higher risk myelodysplastic syndromes (MDS), chronic myelomonocytic leukemia (CMML) or primary myelofibrosis (PMF).

* Note: PMF patients must have failed ≥ 1 of the 4 Food and Drug Administration (FDA)-approved Janus kinase (JAK) Inhibitors for MF (i.e. ruxolitinib, fedratinib, pacritinib, momelotinib) to be eligible. MDS and CMML patients must have failed hypomethylating agent-based therapy, if eligible.
* Note: Higher risk is defined as intermediate or higher risk by international prognostic scoring system (IPSS-R) or moderate high or higher risk as per molecular internal prognostic scoring system (IPSS-M).
* T cell lymphoma (peripheral and cutaneous), or mantle cell lymphomas. Patients must have failed ≥ 2 lines of therapy.
* Primary central nervous system (CNS) lymphoma who has failed ≥ 2 lines of therapy.
* Relapsed or refractory follicular lymphoma; or Waldenstrom macroglobulinemia/lymphoplasmacytic lymphoma. Must have failed ≥ 2 lines of therapy.
* Patients with Waldenström macroglobulinemia who have received or are not eligible for a Bruton tyrosine kinase (BTK)-inhibitor therapy.
* Relapsed or refractory chronic lymphocytic leukemia (CLL)/small lymphocytic lymphoma (SLL) who have failed ≥ 2 lines of therapy and have been treated with at least one prior line of a BTK inhibitor and/or a B-cell lymphoma 2 (BCL2) inhibitor. Need documented CLL/SLL requiring treatment according to International Workshop on Chronic Lymphocytic Leukemia (iwCLL) guidelines 2018.

* NOTE: Use of oral steroids up to 20 mg of daily will be allowed for patients who are discontinuing BTK inhibitors just prior to the registration. This is not mandatory and should be done at the discretion of patient's treating physician.

* Note: All patients in the above disease groups may be on corticosteroids at the investigator's discretion
* PRE-REGISTRATION: Histopathological or cytological confirmation of diseases
* PRE-REGISTRATION: Willingness to provide mandatory blood, bone marrow aspirate, saliva, and tissue specimens for correlative research, as applicable to the disease site
* PRE-REGISTRATION: Ability to swallow pills
* REGISTRATION: Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, or 2
* REGISTRATION: Life expectancy of ≥ 3 months
* REGISTRATION: Measurable or assessable disease:

* For histiocytic neoplasms and lymphoma-measurable disease is defined as measurable by CT (dedicated CT or the CT portion of a PET/CT) or MRI: To be considered measurable, there must be at least one lesion that has a single diameter of ≥ 1.5 cm for non-CNS disease. For CNS involved disease, MRI confirmation with any size would be appropriate.

* NOTE: Skin lesions can be used if the area is ≥ 1.5 cm in at least one diameter and photographed with a ruler. Patients with assessable disease by PET/CT are also eligible as long as the assessable disease is biopsy proven lymphoma or histiocytic/dendritic cell neoplasms.
* For all other eligible diseases listed-N/A
* REGISTRATION: Hemoglobin ≥ 8.0 g/dL (obtained ≤ 14 days prior to registration)
* REGISTRATION: Absolute neutrophil count (ANC) ≥ 1.0 x 10\^9/L (obtained ≤ 14 days prior to registration)
* REGISTRATION: Platelet count ≥ 80 x 10\^9/L (obtained ≤ 14 days prior to registration)
* REGISTRATION: White blood cell (WBC) ≥ 2.5 x 10\^9/L (obtained ≤ 14 days prior to registration)
* REGISTRATION: Total bilirubin ≤ 1.5 x upper limit of normal (ULN) (obtained ≤ 14 days prior to registration)
* REGISTRATION: Alanine aminotransferase (ALT), aspartate transaminase (AST), and alkaline phosphatase (ALP) ≤ 2.5 x ULN (≤ 5 x ULN for patients with liver involvement) (obtained ≤ 14 days prior to registration)
* REGISTRATION: Serum creatinine of ≤ 1.5 x ULN and calculated creatinine clearance of ≥ 50 mL/min using the Cockcroft-Gault formula (obtained ≤ 14 days prior to registration)
* REGISTRATION: Negative urine or serum pregnancy test done ≤ 7 days prior to registration, for persons of childbearing potential only
* REGISTRATION: Sexually active patients and their partners must use an effective method of contraception associated with a low failure rate prior to study entry and for the duration of study participation and for at least 3 months after the last dose of study drug.

* Note: The following are considered effective contraceptives: oral contraceptive pill; condom plus spermicide; diaphragm plus spermicide; patient or partner surgically sterile; patient or partner more than 2 years postmenopausal; or injectable or implantable agent/device
* REGISTRATION: Provide written informed consent
* REGISTRATION: Ability to complete questionnaire(s) by themselves or with assistance
* REGISTRATION: Willing to return to the enrolling institution for follow-up (during the Active Monitoring Phase of the study).

Exclusion Criteria:

* PRE-REGISTRATION: Myeloproliferative neoplasm (MPN) patients with known active CNS metastases and/or carcinomatous meningitis.

* Note: Histiocytosis and lymphoma patients who are on steroids are allowed to enroll
* REGISTRATION: Any of the following because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effect on the developing fetus and newborn are unknown:

* Pregnant persons
* Nursing persons
* Persons of childbearing potential (and persons able to father a child) who are unwilling to employ adequate contraception
* REGISTRATION: New York Heart Association Class III or IV cardiac disease, or myocardial infarction, severe unstable angina, coronary/peripheral artery bypass graft, congestive heart failure ≤ 6 months prior to registration
* REGISTRATION: Corrected QT interval (using Fridericia's correction formula) (QTcF) of \> 470 msec
* REGISTRATION: Known active infection with human immunodeficiency virus (HIV), Human T-lymphotropic virus 1 (HTLV-1), hepatitis B virus (HBV), or hepatitis C virus (HCV):

* Active infection with (HIV) and CD4+ T-cell count \< 350 μL.
* Patients with a detectable HIV viral load and not on antiretroviral therapy (ART) for ≥ 4 weeks.
* Exceptions:

* Patients with a history of hepatitis B or C are allowed if HBV deoxyribonucleic acid (DNA) or HCV ribonucleic acid (RNA) are undetectable.
* Patients with active HIV infection and CD4+ T-cell count ≥ 350 μL who are on active antiretroviral treatment
* REGISTRATION: Active, uncontrolled bacterial, viral, or fungal infections, requiring systemic therapy
* REGISTRATION: Concomitant use of strong inhibitors and inducers of CYP1A2, CYP2C19, CYP2D6, and strong inhibitors and inducers of CYP3A4 within five half-lives of the active drug prior to registration and throughout the trial.

* Note: Strong inhibitors and inducers of CYP3A4 should be discontinued for five half-lives of the active drug prior to starting study drug and avoided throughout the trial
* REGISTRATION: Concomitant use of any herbal supplements.

* Note: Supplements taken prior to starting study drug should be discussed with the Principal Investigator as varied washout periods may be clinically indicated and necessary
* REGISTRATION: Any of the following prior therapies used as primary cancer treatment:

* Targeted therapeutics other than monoclonal antibodies (e.g., kinases inhibitors) ≤ 2 weeks prior to registration.
* Monoclonal antibodies ≤ 6 weeks, or ≥ 5 half-life, whichever is shorter, prior to registration.
* Chemotherapy ≤ 4 weeks prior to registration (6 weeks for nitrosoureas or Mitomycin C.
* Surgery ≤ 4 weeks prior to registration
* Any investigational therapy ≤ 4 weeks prior to registration
* Radiation therapy ≤ 4 weeks prior to registration

* Exceptions:

* Palliative radiation therapy ≥ 2 weeks prior to registration for control of tumor mass related symptoms (e.g., pain control from a discrete bone metastasis) allowed, unless the radiation field includes organs for which the radiation therapy could result in certain direct organ toxicities (e.g., radiation induced esophagitis), which could complicate the interpretation of the Q702 safety profile.
* Radiation induced toxicities which could interfere with the interpretation of the Q702 safety profile should recover to ≤ grade 1 before registration.
* Patients receiving palliative radiation intended to reduce the risk of a potential pathological fracture should be allowed ≥ 4 weeks from the last radiation therapy treatment to recover from any radiation induced toxicity and to allow for an adequate period of observation relative to the potential risk of a pathological fracture
* REGISTRATION: Failure to recover from acute, reversible effects of prior therapy to ≤ grade 1 or patient baseline prior to registration.

* NOTE: Patient with chronic effects such as neuropathy, fatigue, keratitis/keratopathy, anorexia, etc. are allowed
* REGISTRATION: Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens
* REGISTRATION: Active retinal pigment epithelium (RPE)/photoreceptor disorders such as retinitis pigmentosa, cone-rod dystrophies, Bests dystrophy, Stargardt disease (STGD), macular degeneration, retinal detachment, and opaque cornea. Exceptions:

* Mild blurry vision, either age-related or due to ocular or systemic disorder (e.g., diabetes, dry eyes, cataracts, uncorrected refraction abnormality) may be allowed at the discretion of the ophthalmologist if deemed as not constituting evidence of pre-existing retinopathy (e.g., severe nonproliferative or proliferative diabetes retinopathy) or a condition with the potential to cause a predisposition to drug-induced retinopathy. \[e.g., severe retinal vascular disease with scattered intraretinal hemorrhages, cotton wool-spots and intraretinal microvascular abnormalities (IRMA)\]
* Patients with only one assessable eye and no evidence of pre-existing retinopathy may be allowed at the discretion of the principal investigator
* REGISTRATION: Active second malignancy requiring treatment that would interfere with the assessment of the response of the primary cancer or interpretation of the safety of this protocol therapy