Inclusion Criteria:
1. Male or female and ≥ 18 years of age
2. Have provided written informed consent to participate in the study
3. Diagnosis of phenotypic classical FAP with disease involvement of the duodenum or the residual colon/rectum/pouch as the primary disease site.
4. Genetic diagnosis of FAP with APC gene mutation (Part 2 only).
5. Has undergone colectomy or subtotal colectomy
6. Spigelman Classification Stage II or higher.
7. Investigator/Participant agrees to leave polyps ≤10 mm unresected during endoscopies performed at Screening and while on study
8. Have no significant cardiovascular abnormalities at Screening:
1. Left ventricular ejection fraction \>50% as determined on screening echocardiogram (ECHO)/ multi-gated acquisition (MUGA)
2. A QT interval corrected for heart rate using the Fridericia formula (QTcF) \< 450 msec in men and \<470 milliseconds (msec) in women.
9. Have no significant hematopoietic abnormalities at Screening:
1. White blood cell count (WBC) ≥ 3,000/cubic millimeters (mm\^3) (non-black populations); 2,700/mm\^3 (black populations)
2. Platelet count ≥ 120,000/mm\^3
3. Hemoglobin ≥ 10.0 grams (g)/deciiter (dL)
4. No history of clinical coagulopathy.
10. Have no significant hepatic abnormalities at Screening:
1. Total bilirubin ≤ 1.5 \* upper limit of normal (ULN) (individuals with Gilbert syndrome may be enrolled)
2. Aspartate transaminase (AST), alanine transaminase (ALT), alkaline phosphatase (ALP) ≤ 2.0 \* ULN.
11. Have no significant renal abnormalities at Screening: serum creatinine ≤ 1.5 times \* ULN.
12. Female participants who are women of childbearing potential (WOCBP) must have a negative serum pregnancy test at screening and a negative urine pregnancy test within 24 hours before the first dose of study drug. If the urine test is positive or cannot be confirmed negative, a serum pregnancy test will be required and must be negative for the participant to be eligible.
13. All participants must be willing to follow the contraceptive guidance in the protocol and must not be lactating or planning to attempt to become pregnant during the study or for a further period of 4 months after the last dose of study drug or impregnate someone during this study or for a further period of 14 weeks after the last dose of study drug.
14. Absence of gross blood in stool at Screening; red blood on toilet paper only is acceptable.
15. Participant must be willing to discontinue use of non-steroidal anti-inflammatory agents (NSAIDs) 6 weeks prior to Study Day 1 and remain off NSAIDs throughout the treatment period of the study (use of aspirin ≤ 700 milligrams \[mg\] week is allowed.)
Exclusion Criteria:
1. Has any clinically significant laboratory abnormality, medical or psychiatric illness which, in the opinion of the Investigator, could interfere with the conduct or interpretation of the study or put the participant at risk.
2. Has had prior pelvic irradiation.
3. Has gastrointestinal disease or recent gastrointestinal procedure that could interfere with oral absorption of REC-4881, including difficulty swallowing capsules.
4. Has received treatment with other investigational agents within the 4 weeks prior to Study Day 1 or a period during which the investigational agent has not been cleared from the body (that is, at least a period of 5 half-lives, if known), whichever is longer.
5. Treatment with other FAP-directed drug therapy (such as off-label use of Balsalazide) within 8 weeks of screening endoscopy (Part 2 only) or had a Whipple procedure.
6. Is currently under treatment for desmoid tumors.
7. Use of omega-3 fatty acids or oral corticosteroids prior to Study Day 1
8. Use of strong cytochrome P3A (CYP3A) inhibitors or inducers prior to Study Day 1
9. History of an ongoing or newly diagnosed eye abnormality, including:
1. Retinal pathologies such as diabetic retinopathy, veno-occlusion, or macular edema
2. Corneal pathologies such as herpes keratitis, corneal dystrophy, corneal erosions, corneal degeneration, active or recurrent keratitis, or uveitis (intermittent, posterior, and/or panuveitis)
3. Other clinically significant ophthalmologic abnormalities (for example, retinal detachment) or has findings at Screening. \[Participants with corrected myopia may be enrolled.\]
10. Has cancer at screening endoscopy in gastrointestinal (GI) tract (including stomach, duodenum, and colon/rectum/pouch) (Part 2 only).
11. Has a large polyp (\>1 centimeter \[cm\]) not amenable to complete removal
12. Has active pancreatitis secondary to pancreatic duct obstruction
13. Has active gall bladder disease
14. Is pregnant, lactating or is planning to attempt to become pregnant during this study or within 4 months after the last dose of study drug (women) or is planning to attempt to impregnate someone or donate sperm during the study or within 14 weeks after the last dose of study drug (men).
15. Has had major surgery prior to Study Day 1
16. Has an active infection requiring systemic therapy.
17. Has known hypersensitivity to the study drug or its excipients.
18. Has a history of alcohol or substance abuse within 1 year prior to screening for study participation, or is currently using alcohol, drugs of abuse, or any prescribed or over-the-counter medication in a manner which, in the opinion of the Investigator, indicates abuse.
19. Received treatment with another mitogen-activated protein kinase (MEK) inhibitor 8 weeks prior to Screening and throughout the treatment period of the study.
20. Any of the following known active infections:
1. Human immunodeficiency virus (HIV) not optimally controlled or treated. Participants with HIV who are on sustained stable antiretrovirals (for \>4 weeks) and have cluster of differentiation (CD)4+ counts ≥ 350 cells/microliter (μL) may be enrolled. No HIV testing is required unless clinically indicated or mandated by local health authority.
2. Chronic hepatitis B virus (HBV) infection with surface antigen positive: participants with a prior history of treated HBV infection who are hepatitis B surface antigen-negative may be enrolled. No testing is required for hepatitis B unless clinically indicated or mandated by local health authority.
3. Chronic hepatitis C virus (HCV) infection: untreated or on active treatment. Participants with a prior history of treated HCV infection who are HCV RNA-undetectable may be enrolled. No testing is required for hepatitis C unless clinically indicated or mandated by local health authority.
21. Has a severe or uncontrolled medical condition (for example, dermatologic disease, etc.) that, in the opinion of the Investigator, would pose a significant clinical risk for the participant.
22. Use of strong Breast Cancer Resistance Protein (BCRP) or Multidrug Resistance-Associated Protein 2 (MRP2) inhibitors within 14 days of Study Day 1 and throughout the treatment period of the study.
23. Clinically significant cardiovascular disease ≤ 6 months before first dose
1. Myocardial infarction or unstable angina
2. Clinically significant cardiac arrhythmias
3. Uncontrolled hypertension: systolic blood pressure (SBP) \> 180 millimeters of mercury (mmHg), diastolic blood pressure (DBP) \> 100 mmHg
4. Pulmonary embolism, symptomatic cerebrovascular events or any other serious cardiac condition (for example, pericardial effusion or restrictive cardiomyopathy)
5. QTcF prolongation \>450 msec in males and \>470 msec in females at screening or history of long QTc syndrome
6. Congestive heart failure (New York Heart Association class III-IV)
7. Myocarditis / clinically significant pericarditis.
8. Atrial enlargement.
