Testing RG1-VLP Vaccine to Prevent HPV-related Cancers

Inclusion Criteria: * Women, age 18 - 60 years. Because no dosing or adverse event (AE) data is currently available for the use of RG1-VLP in humans, children and adolescents are excluded from this study * White blood cell (WBC) between 3000/mm\^3 - institutional upper limit of normal * Hemoglobin (Hgb) between 10 g/dl - institutional upper limit of normal * Platelets \>= 100,000/mm\^3 * Serum creatinine within institutional normal limits * Bilirubin =\< 2x institutional upper limit of normal * Alanine aminotransferase (ALT) =\< 2x institutional upper limit of normal * Aspartate aminotransferase (AST) =\< 2x institutional upper limit of normal * Human immunodeficiency virus (HIV)-1/HIV-2 negative * Hepatitis B and hepatitis C negative * The effects of RG1-VLP vaccination on the developing human fetus at the proposed doses are unknown. For this reason, all women of childbearing potential will have a pregnancy test and all heterosexually active women 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 * The following persons are not considered to be able to bear children and are therefore eligible to participate without the use of concurrent birth control: * Female with bilateral oophorectomy and/or hysterectomy * Female with fallopian tubes cut, tied or sealed * Female with sterilization implant (e.g. Adiana, Essure) placed \> 3 months prior to randomization * Female post-menopausal (\> 1 year since last menses or prior laboratory follicle stimulating hormone \[FSH\] value per institutional range indicating post-menopausal) * Eastern Cooperative Oncology Group (ECOG) performance status of =\< 1 * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * History of any of the following: * Prior or current genital warts * Treatment for anogenital intraepithelial neoplasia (cervical intraepithelial neoplasia \[CIN\], anal intraepithelial neoplasia \[AIN\], vaginal intraepithelial neoplasia \[VAIN\], vulvar intraepithelial neoplasia \[VIN\]) * Systemic cancer treatment within the prior year * History of anaphylaxis to vaccines * Any prior vaccination with Gardasil, Gardasil-9, or Cervarix or other HPV vaccine * Receipt of blood products within 3 months of enrollment, or continuing plasma donation * Participants receiving any other investigational agents * History of allergic reactions attributed to compounds of similar chemical or biologic composition to the adjuvant or to RG1-VLP * Uncontrolled intercurrent illness or psychiatric illness/social situations that would limit compliance with study requirements or preclude protocol vaccination * Pregnant women or actively lactating women are excluded from this study because RG1-VLP is a vaccine with the potential for teratogenic or abortifacient effects * Planned receipt of any inactivated vaccine in the 2 weeks preceding and the 2 weeks following any trial vaccination * Planned receipt of any live attenuated vaccine in the 4 weeks preceding and the 4 weeks following any trial vaccination * Women with a history of bleeding disorders or use of anticoagulants (aspirin is acceptable) * Had prior medical diagnoses: * Rheumatoid arthritis or other auto-immune disease * Congenital or acquired immunodeficiency * Collagen vascular disease * Following medical treatments: * Current use of immunosuppressive drugs including corticosteroid use (inhaled or topical steroids are permitted) * Unrecovered major infections and/or surgical procedures