Study of Miransertib (MK-7075) in Participants With PIK3CA-related Overgrowth Spectrum and Proteus Syndrome (MOSAIC) (MK-7075-002)

Inclusion Criteria: Part A * Signed informed consent and, when applicable, signed assent * Male or female participants ≥ 2 years old with body surface area (BSA) of ≥ 0.33 m\^2 * Have a clinical diagnosis of PROS or PS with documented somatic PIK3CA or serine-threonine protein kinase (AKT1) mutations * Archival or fresh overgrowth tissue sample available to be shipped to Sponsor or designee * Have poor prognosis, significant morbidity, and/or progressive disease (e.g., worsening of the disease/increase in number or size of the overgrowth lesions in the last 12 months) * Have measurable disease (at least one overgrowth lesion that can be accurately measured in size by imaging and/or linear or circumference measure) * Adequate organ function based on screening laboratory values * 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 * Ability to complete the Quality of Life (QoL) questionnaires by the participant or his/her caregiver Part B: * Signed consent form and when applicable, signed assent * Archival or fresh overgrowth tissue sample available to be shipped to Sponsor or designee * Except for Cohort 4, clinically progressive or worsening disease defined as an increase in number or size of the o…