A Study of Carboplatin, PLD and Everolimus in Certain Gynecologic Cancer

Inclusion Criteria: * Histologically confirmed epithelial ovarian, fallopian tube, or primary peritoneal carcinoma * Patients must have had exactly one prior platinum/taxane-based chemotherapeutic regimen for management of primary disease, and must be in first relapse; first relapse must occur \>= six months from completion of front-line platinum-based therapy; (time measured from last platinum dose; for example, patients receiving a biologic or chemotherapeutic agent after completion of platinum-based therapy as part of upfront therapy would be eligible based on time from last dose of platinum chemotherapy; in this situation, patients must be at least four weeks from last dose of a biologic agent); relapse cannot be based on rising cancer antigen (CA)- 125 alone; there must be radiographic evidence of recurrent disease * Measurable disease as per Response Evaluation Criteria In Solid Tumors (RECIST) v1.1 criteria or non-measurable disease with symptomatic malignant pleural effusion or malignant ascites; if only site of disease is a pleural effusion, cytologic confirmation of recurrence should be obtained * Patients must not have any major surgery or radiation therapy within 14 days of start of study treatment * All acute toxicities from prior therapy with the exception of alopecia must have resolved to =\< grade 1 * Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * Absolute neutrophil count (ANC) \>= 1500 * Platelets \>= 100K * Serum total bilirubin =\< 1.5x upper limit of normal (ULN) * Serum transaminase (aspartate aminotransferase \[AST\]/serum glutamic oxaloacetic transaminase \[SGOT\], alanine aminotransferase \[ALT\]/serum glutamic pyruvic transaminase \[SGPT\]) activity =\< 2.5 x ULN * International normalized ratio (INR) =\< 1.5 and partial thromboplastin time (PTT) =\< 1.5 x ULN for patients who are not being treated with therapeutic anticoagulation; therapeutic or prophylactic anticoagulation is allowed if a patient has been on a stable dose of low molecular weight (LMW) heparin for \> 2 weeks at the time of randomization; subjects on therapeutic or prophylactic anticoagulation including warfarin will have PTT and INR as determined by the Investigator; prophylactic use of an anticoagulant to maintain patency of a vascular access device is also allowed) * Serum creatinine =\< 2.0 * Creatinine clearance \> 60 ml/min * Left ventricular ejection fraction (LVEF) \> lower limit of normal (LLN) on multi gated acquisition scan (MUGA) * Ability to understand and willingness to sign a written informed consent document * Ability to take oral medication * Fasting serum cholesterol \< 300 mg/dL and triglycerides \< 2.5 x ULN; Note: in case one or both of these thresholds are exceeded, the patient can be included after initiation of appropriate lipid lowering medication if on repeat analysis, both levels fall within parameters * Able and willing to comply with testing and treatment as outlined in this protocol Exclusion Criteria: * Patients with more than one prior chemotherapy regimen for management of primary disease * Patients who have received a prior mammalian target of rapamycin (mTOR) inhibitor * Chronic treatment with systemic steroids or other immunosuppressive agents; Note: topical or inhaled steroids are allowed * Uncontrolled brain or leptomeningeal metastases, including those who continue to require glucocorticoids for brain or leptomeningeal metastases * Other malignancies =\< 3 years prior to registration except for adequately treated carcinoma of the cervix or basal or squamous carcinomas of the skin * Other concurrent severe and/or uncontrolled medical disease which could compromise participation in the study; examples include, but are not limited to: uncontrolled diabetes defined as fasting serum glucose \> 1.5 x ULN; uncontrolled hypertension, or greater than 150/100 in spite of antihypertensive therapy; active (acute or chronic) or uncontrolled severe infection; unstable angina pectoris, symptomatic congestive heart failure (New York Heart Association Class III or IV); ventricular arrhythmias, active ischemic heart disease, myocardial infarction within six months; liver disease such as cirrhosis, chronic active hepatitis or chronic persistent hepatitis * Known history of human immunodeficiency virus (HIV) seropositivity as these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy and the potential pharmacokinetic interaction between antiretroviral therapy and the investigational agent * Known history of Hepatitis B or C as these patients may be at risk of disease reactivation when treated with the chemotherapy and/or the investigational agent * Patients should not receive immunization with attenuated live vaccines =\< 7 days of study entry or during study period * Impairment of gastrointestinal function or gastrointestinal disease that may significantly alter the absorption of RAD001 (i.e. ulcerative disease, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome or small bowel resection sufficient to impair absorption of drug) * Patients with clinical symptoms of gastrointestinal obstruction and who require parenteral hydration/nutrition * Patients with an active bleeding diathesis * Women who are pregnant or breast-feeding, or women able to conceive and unwilling to practice an effective method of birth control; (women of childbearing potential must have a negative urine or serum pregnancy test within =\< 7 days prior to administration of RAD001); oral, implantable or injectable contraceptives may be affected by cytochrome P450 interactions and are therefore not considered effective for this study * History of noncompliance with medical regimens * Patients with a known hypersensitivity to any of the study agents * Patients unwilling or unable to comply with the outlined protocol * Patients with psychiatric illness or social situations that would limit compliance with study requirements