Inclusion Criteria:

          -  Patients must have histologically- or cytologically-confirmed diagnosis of KRAS or
             NRAS mutation-positive malignancy that is metastatic or unresectable and for which
             standard curative measures do not exist or are no longer effective; patients must have
             activating mutations affecting codons 12, 13, 61, or 146 as determined in a Clinical
             Laboratory Improvement Amendments (CLIA)-certified lab to be eligible for this study

          -  Patients must have measurable disease by Response Evaluation Criteria in Solid Tumors
             (RECIST), defined as 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 by chest x-ray or as >= 10 mm with computed tomography
             (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam

          -  Participants must have received at least one line of prior systemic chemotherapy and
             must have experienced documented radiographic progression or intolerance on this
             therapy

          -  Paired pre-treatment and post-treatment biopsies are required for all patients on Part
             1 and first 15 patients in Part 2; participants must have available archival tumor
             tissue (at least 20 unstained slides); if archival tissue is not available or is found
             not to contain tumor tissue, a fresh biopsy is required; if a patient is having a
             tumor biopsy, less than 20 unstained slides are acceptable with approval of the
             principal investigator (PI); biopsies will only be performed in a given patient if
             they are not deemed to involve unacceptable risk based on the sites of disease and
             other concurrent medical conditions

          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 1

          -  Life expectancy of greater than 3 months

          -  Able to swallow and retain orally-administered medication and does not have any
             clinically significant gastrointestinal abnormalities that may alter absorption such
             as malabsorption syndrome or major resection of the stomach or bowels

          -  All prior treatment-related toxicities must be Common Terminology Criteria for Adverse
             Events version 4 (CTCAE v 4) grade =< 1 (except alopecia) at the time of enrollment;
             this requirement to return to =< grade 1 does not apply to immune checkpoint inhibitor
             related endocrinopathies (e.g. thyroiditis, hypophysitis, etc.) that necessitate
             hormone replacement therapy including, but not limited to levothyroxine, cortisol, and
             testosterone; CTCAE v5.0 will be utilized beginning April 1, 2018

          -  Leukocytes >= 3,000/mcL

          -  Absolute neutrophil count (ANC) >= 1,200/mcL (subjects may be treated with
             hematopoietic growth factors to achieve or maintain this level)

          -  Hemoglobin >= 9 g/dL

          -  Platelets >= 100 x 10^9/L

          -  Albumin >= 2.5 g/dL

          -  Total bilirubin =< 1.5 x institutional upper limit of normal (ULN) (patients with
             Gilbert's syndrome may have serum bilirubin > 1.5 x ULN)

          -  Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 2.5 x
             institutional ULN

          -  Serum creatinine =< 1.5 mg/dL OR calculated creatinine clearance (Cockcroft-Gault
             formula) >= 50 mL/min OR 24-hour urine creatinine clearance >= 50 mL/min

          -  Prothrombin time (PT)/international normalized ratio (INR) and partial thromboplastin
             time (PTT) =< 1.2 x institutional ULN

          -  Left ventricular ejection fraction >= institutional lower limit of normal (LLN) by
             echocardiogram (ECHO) or multi gated acquisition scan (MUGA)

          -  The effects of trametinib and navitoclax on the developing human fetus are unknown.
             For this reason, women of child-bearing potential and men with a female partner of
             child bearing potential must agree to use adequate contraception using one of the
             methods listed below prior to study entry, for the duration of study participation,
             and up to 4 months following completion of therapy

               -  Total abstinence from sexual intercourse (minimum one complete menstrual cycle
                  prior to study drug administration)

               -  Vasectomized male subject or vasectomized partner of female subjects

               -  Hormonal contraceptives (oral, parenteral, transdermal or vaginal ring) for at
                  least 3 months prior to study drug administration; if the subject is currently
                  using a hormonal contraceptive, she should also use a barrier method during this
                  study and for 1 month after study completion

               -  Intrauterine device (IUD)

               -  Double-barrier method: male condom plus diaphragm or vaginal cap with spermicide
                  (contraceptive sponge, jellies or creams)

               -  Men with a female partner of childbearing potential must have either had a prior
                  vasectomy or agree to use effective contraception; additionally, male subjects
                  (including those who are vasectomized) whose partners are pregnant or might be
                  pregnant must agree to use condoms for the duration of the study and for 4 months
                  following completion of therapy

          -  Women of childbearing potential must have a negative serum pregnancy test within 7
             days prior to initiation of treatment; women will be considered not of childbearing
             potential if they are surgically sterile (bilateral oophorectomy or hysterectomy)
             and/or post-menopausal (amenorrheic for at least 12 months); should a woman become
             pregnant or suspect she is pregnant while she or her partner is participating in this
             study, she should inform her treating physician immediately; the potential hazard to
             the fetus should be explained to the patient and partner (as applicable)

          -  Ability to understand and the willingness to sign a written informed consent document

        Exclusion Criteria:

          -  History of another malignancy; exception: patients who have been disease-free for 3
             years, or patients with a history of completely resected non-melanoma skin cancer or
             any carcinoma in situ and/or patients with indolent second malignancies, are eligible;
             consult the Cancer Therapy Evaluation Program (CTEP) medical monitor if unsure whether
             second malignancies meet the requirements specified above

          -  History of interstitial lung disease or pneumonitis

          -  Any major surgery, extensive radiotherapy (> 15 days of treatment), chemotherapy with
             delayed toxicity, biologic therapy, or immunotherapy within 21 days prior to first
             dose of study treatment and/or daily or weekly chemotherapy without the potential for
             delayed toxicity within 14 days prior to first dose of study treatment

          -  Use of other investigational drugs within 28 days (or five half-lives, whichever is
             shorter; with a minimum of 14 days from the last dose) preceding the first dose of
             study drug(s) and during the study

          -  Patients with known brain metastases should be excluded from this clinical trial
             because of their poor prognosis and because they often develop progressive neurologic
             dysfunction that would confound the evaluation of neurologic and other adverse events;
             exception: patients with brain metastases will be allowed on study if they have
             clinically controlled neurologic symptoms, defined as surgical excision and/or
             radiation therapy followed by 21 days of stable neurologic function and no evidence of
             central nervous system (CNS) disease progression as determined by computed tomography
             (CT) or magnetic resonance imaging (MRI) within 21 days prior to the first dose of
             study drug

          -  Have a known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs
             chemically related to trametinib, or excipients or to dimethyl sulfoxide (DMSO), or to
             compounds of similar chemical or biologic composition to navitoclax

          -  Current use of a prohibited medication; the following medications or non-drug
             therapies are prohibited:

               -  Other anti-cancer therapy while on study treatment; (note: megestrol [Megace] if
                  used as an appetite stimulant is allowed)

               -  Concurrent treatment with bisphosphonates is permitted; however, treatment must
                  be initiated prior to the first dose of study therapy; prophylactic use of
                  bisphosphonates in patients without bone disease is not permitted, except for the
                  treatment of osteoporosis

               -  Because the composition, pharmacokinetics (PK), and metabolism of many herbal
                  supplements are unknown, the concurrent use of all herbal supplements is
                  prohibited during the study (including, but not limited to, St. John's wort,
                  kava, ephedra [ma huang], ginkgo biloba, dehydroepiandrosterone [DHEA], yohimbe,
                  saw palmetto, or ginseng)

               -  Due to the expected dose-limiting toxicity of thrombocytopenia, the following
                  concomitant medications are not allowed during navitoclax administration:
                  Warfarin, clopidogrel (plavix), ibuprofen, tirofiban (aggrastat), and other
                  anticoagulants, drugs, or herbal supplements that affect platelet function are
                  excluded, with the exception of low-dose anticoagulation medications (such as
                  heparin) that are used to maintain the patency of a central intravenous catheter;
                  aspirin will not be allowed within 7 days prior to the first dose of navitoclax
                  or during navitoclax administration; however, subjects who have previously
                  received aspirin therapy for thrombosis prevention may resume a low dose (i.e.,
                  maximum 100 mg QD) of aspirin if platelet counts are stable (>= 50,000/mm^3)
                  through 6 weeks of navitoclax administration; all decisions regarding treatment
                  with aspirin therapy will be determined by the investigator in conjunction with
                  the medical monitor

          -  Preclinical studies indicate that navitoclax is metabolized by CYP3A4, is a moderate
             inhibitor of CYP2C8, and is a strong inhibitor of CYP2C9; therefore, caution should be
             exercised when dosing navitoclax concurrently with CYP2C8 and CYP2C9 substrates;
             common CYP2C8 substrates include paclitaxel, statins, and glitazones, whereas CYP2C9
             substrates include phenytoin and warfarin; when possible, investigators should switch
             to alternative medications or monitor the patients closely (particularly in the case
             of medications that have a narrow therapeutic window such as warfarin; use of warfarin
             is specifically prohibited while on study); CYP3A inhibitors such as ketoconazole and
             clarithromycin are not allowed 7 days prior to the first dose of navitoclax or during
             navitoclax administration

               -  Because the lists of these agents are constantly changing, it is important to
                  regularly consult a frequently-updated list; medical reference texts such as the
                  Physicians' Desk Reference may also provide this information; as part of the
                  enrollment/informed consent procedures, the patient will be counseled on the risk
                  of interactions with other agents, and what to do if new medications need to be
                  prescribed or if the patient is considering a new over-the-counter medicine or
                  herbal product

               -  Patient instructions and information of possible drug interactions will be given
                  to all patients upon enrollment in this study

          -  History or current evidence/risk of retinal vein occlusion (RVO)

          -  History or evidence of cardiovascular risk including any of the following:

               -  Left ventricle ejection fraction (LVEF) < LLN

               -  A QT interval corrected for heart rate using the Bazett's formula QTcB >= 480
                  msec

               -  History or evidence of current clinically significant uncontrolled arrhythmias
                  (exception: patients with controlled atrial fibrillation for > 30 days prior to
                  enrollment are eligible)

               -  History of acute coronary syndromes (including myocardial infarction and unstable
                  angina), coronary angioplasty, or stenting within 6 months prior to randomization

               -  History or evidence of current >= class II congestive heart failure as defined by
                  the New York Heart Association (NYHA) functional classification system

               -  Treatment-refractory hypertension defined as a blood pressure of systolic > 140
                  mmHg and/or diastolic > 90 mmHg which cannot be controlled by anti-hypertensive
                  therapy

               -  Known cardiac metastases

               -  Patients with intra-cardiac defibrillators

          -  Known hepatitis B virus (HBV), or hepatitis C virus (HCV) infection (patients with
             chronic or cleared HBV and HCV infection are eligible); patients with human
             immunodeficiency virus (HIV) are not eligible if on anti-retroviral medications

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac
             arrhythmia, or psychiatric illness/social situations that would limit compliance with
             study requirements

          -  Subject has an underlying condition predisposing them to bleeding or currently
             exhibits signs of clinically significant bleeding

          -  Subject has a recent history of non-chemotherapy-induced thrombocytopenic-associated
             bleeding within 1 year prior to the first dose of study drug

          -  Subject has a significant history of cardiovascular disease (e.g., myocardial
             infarction [MI], thrombotic or thromboembolic event in the last 6 months)

          -  Pregnant women or nursing mothers; animal reproductive studies have not been conducted
             with trametinib or navitoclax; therefore, the study drug must not be administered to
             pregnant women or nursing mothers