Inclusion Criteria:

          -  Patients must have a body surface area of > 0.3 m^2 at the time of enrollment

          -  Existing or recurrent desmoid tumor that is deemed not amenable to surgery without
             significant morbidity and progressed by >= 10% as assessed by RECIST version (v)1.1
             within the 6-month period prior to study enrollment

               -  Patients must have had histologic verification of the desmoid tumor

               -  Patients must have measurable disease by RECIST v1.1 criteria

               -  Patient must have received at least one prior course of systemic therapy for
                  desmoid tumor

          -  Patients must have a Lansky (for patients =< 16 years of age) or Karnofsky (for
             patients > 16 years of age) performance status score of >= 50. Patients who are unable
             to walk because of paralysis, but who are up in a wheelchair, will be considered
             ambulatory for the purpose of assessing performance score

          -  Patients must have fully recovered from the acute toxic effects of all prior
             chemotherapy, immunotherapy, surgery or radiotherapy prior to entering this study.
             Patients may not be using or anticipate using these treatments after the observed
             progression or within the time period stated below

               -  Cytotoxic chemotherapy: must not have received within 2 weeks of entry onto this
                  study (4 weeks if prior nitrosourea)

               -  Small molecule tyrosine kinase inhibitors (e.g., sorafenib, pazopanib, imatinib),
                  rapalogs (e.g., temsirolimus, everolimus, sirolimus) or anti estrogen therapy
                  (e.g., tamoxifen): may not have received within 28 days prior to the first dose
                  of study treatment

               -  Antibodies: >= 21 days must have elapsed from infusion of last dose of antibody,
                  and toxicity related to prior antibody therapy must be recovered to grade =< 1

               -  Biologic (anti-neoplastic agent): at least 7 days since the completion of therapy
                  with a biologic agent

               -  Local regional tumor directed therapy, including, but not limited to small port
                  radiation therapy (RT), radiofrequency ablation, cryotherapy, surgery: at least 2
                  weeks since these therapies and all toxicity must have resolved to grade =< 1. If
                  prior craniospinal RT or if >= 50% radiation of pelvis then >= 6 months must have
                  elapsed. If other substantial bone marrow (BM) radiation, then >= 6 weeks must
                  have elapsed

               -  Stem cell transplant (SCT): No evidence of active graft versus (vs.) host
                  disease. For allogeneic SCT, >= 6 months must have elapsed

               -  No prior gamma-secretase, Notch or beta-catenin inhibitor

               -  Investigational drugs: must not have received investigational drug within 4 weeks
                  of study entry, and all toxicities related to prior therapy must be resolved to
                  grade =< 1 or baseline

          -  Concomitant Medication Restrictions

               -  Steroids: patients who are receiving dexamethasone must be on a stable or
                  tapering dose for at least 2 weeks prior to study entry. Use of steroids for
                  non-tumor indications (e.g., asthma or severe allergic reaction) is permitted

               -  Growth factor(s): must not have received within 1 week of entry onto this study

               -  Patients who are currently receiving drugs that are strong inducers or moderate
                  to strong inhibitors of CYP3A4 are not eligible. Strong inducers or moderate to
                  strong inhibitors of CYP3A4 are not allowed from 14 days prior to enrollment to
                  the end of protocol therapy. Note: CYP3A4 inducing anti-epileptic drugs on a
                  stable dose, are allowed

               -  Must not be receiving non-steroidal anti-inflammatory drugs (NSAIDs) as treatment
                  for desmoid tumor after the observed progression and patient agrees to not use
                  NSAIDs while on study. Occasional use (defined as =< 3 times per week) for
                  treatment of pain is permitted

          -  Peripheral absolute neutrophil count (ANC) >= 1000/uL (within 7 days prior to
             enrollment)

          -  Platelet count >= 100,000/uL (transfusion independent) (within 7 days prior to
             enrollment)

          -  Hemoglobin >= 9.0 g/dL (may receive red blood cell [RBC] transfusions) (within 7 days
             prior to enrollment)

          -  Creatinine clearance or radioisotope glomerular filtration rate (GFR) >= 70
             mL/min/1.73 m^2 or a serum creatinine based on age/gender as follows (within 7 days
             prior to enrollment):

               -  Age: Maximum serum creatinine (mg/dL)

               -  Age: 1 to < 2 years; Maximum serum creatinine (mg/dL): 0.6 (male and female)

               -  Age: 2 to < 6 years; Maximum serum creatinine (mg/dL): 0.8 (male and female)

               -  Age: 6 to < 10 years; Maximum serum creatinine (mg/dL): 1 (male and female)

               -  Age: 10 to < 13 years; Maximum serum creatinine (mg/dL): 1.2 (male and female)

               -  Age: 13 to < 16 years; Maximum serum creatinine (mg/dL): 1.5 (male); 1.4 (female)

               -  Age: >= 16 years; Maximum serum creatinine (mg/dL): 1.7 (male); 1.4 (female)

          -  Total bilirubin =< 1.5 x upper limit of normal (ULN) for age (unless secondary to
             previously diagnosed Gilbert's syndrome) (within 7 days prior to enrollment)

          -  Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase [ALT]) =< 135
             U/L

               -  Note: For the purpose of this study, the ULN for SGPT (ALT) has been set to the
                  value of 45 U/L (within 7 days prior to enrollment)

          -  Adequate cardiac function defined as:

               -  Corrected QT (QTc) interval < 470 ms

               -  No history of congenital or acquired prolonged QTc syndrome

               -  No history of clinically significant cardiac arrhythmias, congestive heart
                  failure, stroke or myocardial infarction within 6 months prior to study entry

          -  All patients and/or their parents or legal guardians must sign a written informed
             consent

          -  All institutional, Food and Drug Administration (FDA), and National Cancer Institute
             (NCI) requirements for human studies must be met

        Exclusion Criteria:

          -  Active or chronic infection within 7 days prior to study entry

          -  Patients with gastrointestinal conditions that might predispose for drug
             intolerability or poor drug absorption (e.g., inability to take oral medication, prior
             surgical procedures affecting absorption (e.g., gastric bypass), malabsorption
             syndrome, and active peptic ulcer disease)

          -  Patients with ulcerative colitis, inflammatory bowel disease, or a partial or complete
             small bowel obstruction

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

          -  Patients with a prior history of malignancy, with the exceptions of desmoid tumor(s)
             and non-melanoma skin cancer, who are not in remission for more than 3 years

          -  Patients who are unable to swallow tablets. Tablets must not be crushed or chewed.
             Administration of nirogacestat via gastrostomy tube or nasogastric tube is not allowed

          -  Patients who in the opinion of the investigator may not be able to comply with the
             safety monitoring requirements of the study

          -  Sexually active female patients of reproductive potential who have not agreed to use 1
             method of highly effective contraceptive (including copper-containing intrauterine
             device, condom with spermicidal foam/gel/film/cream/suppository, bilateral tubal
             ligation, established use of inserted, injected or implanted hormonal method of
             contraception, abstinence, or male sterilization) for the duration of their study
             participation and for at least 6 months after last dose of nirogacestat. A second form
             of contraception (i.e. barrier method) is required for patients who are using hormonal
             contraception as nirogacestat may reduce the efficacy of hormonal contraceptives

          -  Sexually active male patients of reproductive potential who have not agreed to use a
             condom and their female partner who have not agreed to use one of the highly effective
             methods of contraception mentioned above during treatment and for at least 90 days
             after the last dose of nirogacestat

          -  Female patients who are breastfeeding

          -  Female patients who are pregnant. These patients are excluded because there is no
             available information regarding the effects of nirogacestat on the developing human
             fetus and inhibition of gamma-secretase is known to be teratogenic

          -  Female patients of childbearing potential unless a negative pregnancy test result has
             been obtained