MK-7075 (Miransertib) in Proteus Syndrome

* INCLUSION CRITERIA:

All participants in all Cohorts must meet the criteria below:

1. Signed informed consent, and when applicable, signed assent
2. Have a molecular diagnosis of Proteus syndrome with documented somatic AKT1 mutation from a CLIA-certified laboratory or international equivalent.
3. Have progressive and measurable disease (e.g., a measurable manifestation of Proteus syndrome with evidence or report of worsening of manifestation(s)/ in the last 12 months)
4. Adequate organ function as indicated by the following laboratory values:

   Hematological:
   * Hemoglobin (Hgb): \>=10.0 g/dL
   * Glycated hemoglobin (HbA1c): \<=8% (\<=64 mmol/mol)
   * Absolute neutrophil count (ANC): \>=1.5 x 10\^9/L
   * Platelet count \>=150 x 10\^9/L

   Hepatic:
   1. Total bilirubin \<=2 x upper limit of normal (ULN)
   2. Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \<=3 x ULN

   Renal:

   a. Serum creatinine depending on age:

   2-5 years male and female: \<=0.50 mg/dL

   6-10 years male and female: \<=0.59 mg/dL

   11-15 years male and female: \<=1.2 mg/dL

   \>15 years male and female: \<=1.5 mg/dL

   Metabolic (lipids):
   * Cholesterol: \<=400 mg/dL (\<=10.34 mmol/L)
   * Triglyceride: \<=500 mg/dL (\<=5.7 mmol/L)
5. If a female is of child-bearing potential, documentation of a negative pregnancy test is required prior to enrollment. Sexually active participants (male and female) must agree to use double-barrier contraceptive measures, oral contraception, or avoidance of intercourse while on study and for up to 90 days after ending treatment
6. Ability to complete the questionnaires by the participant and/or his/her caregiver

The following specific criteria will be used to assign participants to Cohorts:

Cohort 1 (Proteus syndrome with plantar CCTN) specific criteria:

* Have at least one plantar CCTN that can accurately be measured by standardized photography. The CCTN is defined as a nevus with at least two gyri and three sulci affecting 10% - 70% of the total surface area of the foot.
* Male or female participants age \>=3 and \<=17 years old and BSA of \>=0.33 m\^2

Cohort 2 (Proteus syndrome without plantar CCTN) specific criteria:

* Individuals without an evaluable plantar CCTN
* No prior exposure to miransertib
* Male or female participants age \>=3 years old and BSA of \>=0.33 m\^2

Cohort 3 (Proteus syndrome previously treated with miransertib) specific criteria:

* Participants previously treated with miransertib or currently receiving miransertib under Compassionate Use/Expanded Access or an existing trial (i.e., 16-HG-0014)
* Male or female participants \>=3 years old and BSA of \>=0.33 m\^2

Note: All participants must meet Cohort-related age criteria by/on the date of the first dose, Cycle 1 Day 1

EXCLUSION CRITERIA:

An individual who meets any of the following criteria will be excluded from participation in this study:

1. History of Type 1 or Type 2 uncontrolled diabetes mellitus requiring regular medication (other than metformin or other oral hypoglycemic agents) or fasting glucose \>=160 mg/dL ( if \>12 years old) and \>=180 mg/dL (if \<=12 years old) at the baseline/screening visit
2. History of clinically significant cardiac disorders:

   * Myocardial infarction (MI) or congestive heart failure defined as Class II-IV per the New York Heart Association (NYHA) classification within six months of the first dose of miransertib (MI occurring \>6 months of the first dose of miransertib will be permitted)
   * Grade 2 (per National Cancer Institute \[NCI\] Common Terminology Criteria for Adverse Events \[CTCAE v 5.0\]) or worse conduction defect (e.g., right or left bundle branch block).
3. Major surgery, radiotherapy, chemotherapy, or immunotherapy within four weeks of the first dose of miransertib
4. Any experimental systemic therapy for the purpose of treating Proteus syndrome (e.g., sirolimus, everolimus, high dose steroids, alpelisib) within two weeks of the first dose of miransertib, except for participants who were previously or are currently treated with miransertib under a Compassionate Use/Expanded Access program or existing protocol

   -Participants who were previously treated with or currently are receiving miransertib will be enrolled on Cohort 3 and treated according to the Schedule of Assessments/Study Visits defined in this protocol
5. Intolerance of, or severe toxicity attributed to, AKT inhibitors (e.g., miransertib, uprosertib, afuresertib, ipatasertib)
6. Concurrent severe uncontrolled illness not related to Proteus syndrome

   * Ongoing or active infection
   * Known human immunodeficiency virus (HIV) infection malabsorption syndrome
   * Psychiatric illness/substance abuse/social situation that would limit compliance with study requirements
7. Pregnant or breastfeeding (contraception requirements can be found above and in the informed consent form)
8. Inability to comply with study evaluations or to follow drug administration guidelines
9. Concomitant use of a prohibited medication
10. Regular tobacco use and/or use of cannabidiol/tetrahydrocannabidiol (CBD/THC), and/or vaping products