Testing a Combination of Vaccines for Cancer Prevention in Lynch Syndrome

Inclusion Criteria:

* Participants with LS defined as one of the following:

  * Mutation positive: MLH1, MSH2/EPCAM and MSH6 genotypes with prior history of ≥1 colorectal neoplasms\*\* (tubular or tubulovillous adenoma\[s\] or sessile serrated polyps/adenomas/lesion\[s\] or traditional serrated adenoma\[s\]), and/or colorectal cancer\[s\] (but no active cancer for 6 months) OR
  * PMS2 genotype with prior history of colon cancer(s) (but no active cancer for 6 months)

    * Note: Should be confirmed by pathology report or letter from endoscopist to participant
* Participants must have at least part of the descending/sigmoid colon and/or rectum intact
* Participants must be at least 6 months from any cancer-directed treatment (such as surgical resection, chemotherapy, immunotherapy or radiation). Ongoing adjuvant endocrine therapy is allowed
* Participants \>= 18 years will be enrolled. Because the risk of LS related cancers is very low in participants \< 18 years of age, children and adolescents are excluded from this study
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 70%)
* Leukocytes \>= 3,000/microliter
* Absolute neutrophil count \>= 1,500/microliter
* Platelets \>= 100,000/microliter
* Total bilirubin =\< institutional upper limit of normal

  * Note: Higher bilirubin levels (\<= 3 mg/dL) can be allowed if due to a known benign liver condition, i.e. Gilbert's
* Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 1.5 x institutional upper limit of normal
* Creatinine =\< institutional upper limit of normal or estimated glomerular filtration rate (eGFR) \>= 60 ml/min/1.73m\^2
* The effects of the Tri-Ad5 vaccines and N-803 on the developing human fetus at the recommended therapeutic dose are unknown. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her study physician immediately
* Ability to understand and the willingness to sign a written informed consent document
* Participants must be willing and able to space coronavirus disease (COVID) vaccines at least 2 weeks prior to and 2 weeks after receipt of study agent

Exclusion Criteria:

* History of organ allograft or other history of immunodeficiency
* Known human immunodeficiency virus (HIV) with CD4 count \< 540, hepatitis B virus (HBV), or hepatitis C virus (HCV) infection. Subjects with laboratory evidence of cleared HBV and HCV infection will be permitted. Poorly controlled HIV may prevent an adequate immune response to the vaccine and will be an exclusion criterion
* Subjects requiring systemic treatment with corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 3 months of vaccination
* Participants may not be receiving any other investigational agents
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to adenovirus-based vaccines and N-803
* Uncontrolled intercurrent illness or psychiatric illness/social situations that would limit compliance with study requirements
* Pregnant women are excluded from this study because of the unknown effects of the vaccine and N-803 on the fetus. Because there is an unknown but potential risk for adverse events (AEs) in nursing infants secondary to treatment of the mother with the vaccine plus N-803, breastfeeding should be discontinued if the mother is treated with the vaccine plus N-803
* History of untreated thrombotic disorders
* Participants who experienced severe side effects or allergic reactions to previous adenovirus-based vaccines (such as Johnson and Johnson COVID vaccine) will be excluded
* History of atrial fibrillation
* History of gastrointestinal hemorrhage and intracranial hemorrhage