Inclusion Criteria:

          -  Subjects with advanced or metastatic solid tumors that are refractory to standard
             therapies known to provide clinical benefit. Subjects with hematologic malignancy
             including lymphoma/myeloma will not be enrolled on this study.

          -  Subjects must have one of the following: a. somatic mutations in human epidermal
             growth factor receptor (EGFR, HER2, HER3, and HER4); b. EGFR gene amplification
             (patients with 3+ results on immunohistochemistry testing for EGFR may be allowed to
             enroll if gene amplification results are unavailable); c. HER2 gene amplification
             (patients with 3+ results on immunohistochemistry testing for HER-2 may be allowed to
             enroll if gene amplification results are unavailable); d. somatic mutation in KRAS
             (patients will be enrolled only on neratinib and trametinib combination arm).

          -  Subjects must have measurable disease by Response Evaluation Criteria in Solid Tumors
             (RECIST) version (v) 1.1.

          -  Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-1.

          -  Absolute neutrophil count >= 1500/mL.

          -  Platelets >= 100,000/mL.

          -  Hemoglobin >= 9 g/dL.

          -  Creatinine =< 1.5 X upper limit of normal (ULN).

          -  Total bilirubin =< 1.5 X ULN.

          -  Aspartate aminotransferase (AST/serum glutamic oxaloacetic transaminase [SGOT]) and/or
             alanine aminotransferase (ALT/serum glutamate pyruvate transaminase [SGPT]) =< 2.5 X
             ULN (=< 5 X ULN in subjects with liver metastases).

          -  Subjects must be >= 4 weeks beyond treatment with any chemotherapy or other
             investigational therapy to include hormonal, biological, or targeted agents; or at
             least 5 half-lives from hormonal, biological, or targeted agents, whichever is shorter
             at the time of treatment initiation.

          -  Women of child-bearing potential MUST have a negative serum or urine human chorionic
             gonadotropin (HCG) test unless prior hysterectomy or menopause (defined as 12
             consecutive months of amenorrhea). Subjects should not become pregnant or breastfeed
             while on this study. Sexually active subjects must agree to use contraception for the
             duration of study participation and for 4 months after the last dose of neratinib and
             everolimus, palbociclib or trametinib.

          -  Ability to understand and willingness to sign informed consent form prior to
             initiation of the study and any study procedures.

          -  Only for subjects enrolled in Arm 1 - Neratinib and everolimus: fasting lipid profile:
             cholesterol less than or equal to 350 mg/dL and triglycerides less than or equal to
             400 mg/dL.

          -  Only for subjects enrolled in Arm 1 - Neratinib and everolimus: patients who are
             taking medications with moderate or potent inhibitors or inducers of CYP450 3A4 should
             be off for 5 half-lives prior to starting everolimus.

          -  Only for subjects enrolled in Arm 2 - Neratinib and palbociclib: any prior neuropathy
             should be back to baseline or grade 1.

          -  Only for subjects enrolled in Arm 2 - Neratinib and palbociclib: patients who are
             taking medications with moderate or potent inhibitors or inducers of CYP450 3A4 should
             be off for 5 half-lives prior to starting palbociclib.

          -  Only for subjects enrolled in Arm 3 - Neratinib and trametinib: all skin rash
             (dermatitis acneiform, erythema, xeroderma, eczema) should be at grade 1 when starting
             trametinib treatment.

          -  Only for subjects enrolled in Arm 3 - Neratinib and trametinib: history of retinal
             disorder, dry eye syndrome, or blurry vision need to be evaluated by ophthalmology
             prior to starting treatment.

        Exclusion Criteria:

          -  Subjects who are pregnant or breastfeeding.

          -  Known hepatitis B, hepatitis C or human immunodeficiency virus (HIV) infection.

          -  Inability or unwillingness to swallow pills.

          -  Active infection requiring intravenous (IV) antibiotics or other uncontrolled
             intercurrent illness requiring hospitalization.

          -  Clinically significant gastrointestinal (GI) abnormalities that may alter absorption
             such as malabsorption syndrome or major resection of the stomach or bowels. For
             example, subjects should have no more than 50% of the large intestine removed and no
             sign of malabsorption (e.g. gastrectomy, ileal bypass, chronic diarrhea, Crohn's
             disease, malabsorption, gastroparesis).

          -  Inability to comply with the study and follow-up procedures.

          -  History of cerebrovascular accident (CVA), myocardial infarction or unstable angina
             within the previous 6 months before starting therapy.

          -  Prolongation of QT/ corrected QT (QTc) interval (QTc interval > 450 ms for males or >
             470 ms for females) using the Fridericia method of QTc analysis.

          -  Has known primary brain tumor, active central nervous system (CNS) metastases and/or
             carcinomatous meningitis. Subjects with previously treated brain metastases may
             participate provided they are clinically stable with no neurological symptoms, and are
             not using steroids for at least 7 days prior to trial treatment. This exception does
             not include carcinomatous meningitis which is excluded regardless or clinical
             stability.

          -  Uncontrolled concurrent disease or illness including but not limited to: symptomatic
             congestive heart failure (New York Heart Association [NYHA] class III or IV) per the
             NYHA classification, unstable angina pectoris, clinically significant cardiac
             arrhythmia; unstable or untreated cardiac conditions or ejection fraction of < 50% as
             determined by echocardiogram (ECHO) or multiple gated acquisition scan (MUGA);
             diabetes mellitus (i.e. fasting blood glucose > 220 despite acceptable chronic
             diabetes therapy); psychiatric illness that would limit compliance with study
             requirements, as determined by the investigator.

          -  Participating in any other clinical trials using an investigational product.

          -  Only for subjects enrolled in Arm 1 - Neratinib and everolimus: history of
             hypersensitivity to everolimus.

          -  Only for subjects enrolled in Arm 1 - Neratinib and everolimus: subjects requiring
             therapy with immunosuppressive agents such as anti-tumor necrosis factor alpha (TNFa)
             agents (etanercept, adalimumab), azathioprine, methotrexate, cyclosporine, etc. for
             active autoimmune disorder.

          -  Only for subjects enrolled in Arm 1 - Neratinib and everolimus: Major surgery =< 28
             days prior to treatment with everolimus.

          -  Only for subjects enrolled in Arm 3 - Neratinib and trametinib: albumin less than 3
             Gm/dL.