Inclusion Criteria:

          -  Age >= 18 years old

          -  Life expectancy > 12 weeks

          -  Subjects must be willing and able to comply with scheduled visits, treatment schedule,
             laboratory testing, and other requirements of the study

          -  At least one measurable untreated brain lesion >= 0.5 cm and < 3.0 cm in the longest
             axis according to modified RECIST 1.1

          -  Prior stereotactic radiosurgery (SRS) with up to 3 lesions treated with at least a 14
             day interval is allowed as long as the previous treatment volume does not overlap with
             the current targets

          -  Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG)
             performance scale

          -  Subjects must be free of neurologic signs and symptoms related to metastatic brain
             lesions and must not have required or received systemic corticosteroid therapy in the
             10 days prior to beginning protocol therapy

          -  Prior treatment with immunotherapy and targeted therapy allowed as long as it did not
             include a combination of MEK inhibitor (i) + anti-PD(L)-1 antibody and is > 14 days
             prior to start of protocol therapy. All tumor types will be eligible and included in
             the dose escalation phase. Dose expansions will include 10 patients each from lung,
             breast, and melanoma

          -  Patients with melanoma must have received prior PD-1 based therapy and have evidence
             of progression

          -  Patients with non-small cell lung cancer (NSCLC) must have received prior PD-1 based
             therapy and have evidence of progression

          -  Patients with triple-negative breast cancer (TNBC) and hormone receptor positive (HR+)
             are included (any number of prior lines of therapy-including immuno-oncology [IO]
             naive patients)

          -  For HR+ patients, patients are allowed to receive endocrine therapy with or without
             CDK4/6 inhibitors per treating physician discretion (Arimidex, letrozole, exemestane,
             or fulvestrant)

          -  Systematic radiation therapy is allowed (> 14 day washout)

          -  Prior platinum-based chemotherapy for NSCLC patients is allowed

          -  Absolute neutrophil count (ANC) >= 1500/uL

          -  Platelets >= 100 000/uL

          -  Hemoglobin >= 9.0 g/dL or >= 5.6 mmol/L

               -  Criteria must be met without erythropoietin dependency and without packed red
                  blood cell (pRBC) transfusion within last 2 weeks

          -  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 for participant with creatinine levels > 1.5
             x institutional ULN

               -  Creatinine clearance (CrCl) should be calculated per institutional standard

          -  Total bilirubin =< 1.5 x ULN OR direct bilirubin =< ULN for participants with total
             bilirubin levels > 1.5 x ULN

          -  Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT]) and
             alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 2.5 x
             ULN (=< 5 x ULN for participants with liver metastases)

          -  International normalized ratio (INR) OR prothrombin time (PT) =< 1.5 x ULN unless
             participant is receiving anticoagulant therapy as long as PT or activated partial
             thromboplastin time (aPTT) is within therapeutic range of intended use of
             anticoagulants

          -  Activated partial thromboplastin time (aPTT) =< 1.5 x ULN unless participant is
             receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of
             intended use of anticoagulants

          -  Women of child-bearing potential (WOCBP) must not be breastfeeding and must have a
             negative pregnancy test within 3 days prior to initiation of dosing. She must agree to
             use an acceptable method of birth control from the time of the negative pregnancy test
             up to 120 days after the last dose of study drug. WOCBP must agree to adhere to the
             contraceptive guidance

               -  Note: A female participant is eligible to participate if she is not a woman of
                  childbearing potential

          -  Fertile men must agree to use an acceptable method of birth control while on study
             drug and up to 120 days after the last dose of study drug and also refrain from
             donating sperm during this period

          -  All associated toxicity from previous or concurrent cancer therapy must be resolved
             (to =< grade 1 or baseline) prior to study treatment administration. Steroids for
             physiological replacement are allowed

        Exclusion Criteria:

          -  Patients with clinical or radiographic evidence of leptomeningeal disease

          -  Those who experienced grade 3 or 4 neurotoxicity from prior SRS

          -  Prior external beam radiation to the brain or whole brain radiation

          -  Contraindications to MRI (implanted metal device or foreign bodies) or MRI contrast
             (insufficient renal function or allergy)

          -  Subjects with major medical, neurologic or psychiatric condition who are judged as
             unable to fully comply with study therapy or assessments should not be enrolled

          -  Active secondary malignancy unless the malignancy is not expected to interfere with
             the evaluation of safety and is approved by the principle investigator (PI). Examples
             of the latter include basal or squamous cell carcinoma of the skin, in-situ carcinoma
             of the cervix, and isolated elevation of prostate-specific antigen. Subjects with a
             completely treated prior malignancy and no evidence of disease for >= 2 years are
             eligible

          -  Has a known history of or is positive for hepatitis B (hepatitis B surface antigen
             [HBsAg] reactive) or known active hepatitis C virus infection (note treated and cured
             history of hepatitis C is allowed) (hepatitis C virus [HCV] ribonucleic acid [RNA]
             [qualitative] is detected)

               -  Note: Without known history, testing needs to be performed to determine
                  eligibility. Hepatitis C antibody (Ab) testing is allowed for screening purposes
                  in countries where HCV RNA is not part of standard of care

          -  Has a known history of human immunodeficiency virus (HIV) infection. No HIV testing is
             required unless mandated by local health authority

          -  The use of corticosteroids is not allowed for 10 days prior to initiation of therapy
             (based upon 5 times the expected half-life of dexamethasone) except patients who are
             taking steroids for physiological replacement. If alternative corticosteroid therapy
             has been used, consultation with the PI is required to determine the washout period
             prior to initiating study treatment

          -  Subjects with a condition requiring systemic treatment with either corticosteroids (>
             10 mg daily prednisone equivalent) or other immunosuppressive medications within 14
             days of study initiation. Inhaled or topical steroids, and adrenal replacement steroid
             doses > 10 mg daily prednisone equivalent, are permitted in the absence of active
             autoimmune disease

          -  Major surgical procedure, open biopsy (excluding skin cancer resection), or
             significant traumatic injury within 14 days of initiating study drug (unless the wound
             has healed) or anticipation of the need for major surgery during the study

          -  Non-healing wound, ulcer, or bone fracture

          -  Women who are breast-feeding or pregnant

          -  Subjects with a history of serious intercurrent chronic or acute illness, such as
             cardiac or pulmonary disease, hepatic disease, bleeding diathesis or recent major
             bleeding events or other illness considered by the Investigator as high risk for
             investigational drug treatment

          -  Arterial or venous thrombotic or embolic events such as cerebrovascular accident
             (including transient ischemic attacks), deep vein thrombosis or pulmonary embolism
             within the 6 months before start of study medication (except for adequately treated
             catheter-related venous thrombosis occurring more than 1 month before the start of
             study medication)

          -  History of clinically significant cardiac disease or congestive heart failure > New
             York Heart Association (NYHA) class 2. Subjects must not have unstable angina (anginal
             symptoms at rest) or new-onset angina within the last 3 months or myocardial
             infarction within the past 6 months

          -  Investigational drug use within 14 days (or 5 half-lives, whichever is longer) of the
             first dose of bintrafusp alfa and/or pimasertib

          -  Has a history of (grade 3 or 4) non-infectious pneumonitis that required steroids or
             current pneumonitis

          -  Retinal degenerative disease (hereditary retinal degeneration or age-related macular
             degeneration), history of retinal vein occlusion (RVO) or any eye condition that would
             be considered as risk factor for RVO (e.g. uncontrolled glaucoma or ocular
             hypertension)

          -  Creatine phosphokinase level at baseline National Cancer Institute (NCI) Common
             Terminology Criteria for Adverse Events (CTCAE) grade >= 2 (> 2.5 x ULN - 5 x ULN)
             and/or previous history of myositis or rhabdomyolysis

          -  For NSCLC cohort patients whose tumor exhibit activating EGFR mutation, ALK or ROS
             translocation and have a standard of care molecular targeted therapy available for
             these mutations, will be excluded from this study. Patients who progressed or could
             not tolerate these standard of care molecular targeted agents are eligible for this
             study. Lung adenocarcinoma patients may be consented prior to the EGFR and ALK status
             being known, but EGFR and ALK status must be determined prior to initiating therapy

          -  Administration of live, attenuated vaccine therapies for the prevention of infectious
             diseases within 4 weeks prior to day 1 of treatment and during therapy