Carboplatin, Paclitaxel, and Everolimus in Treating Patients With Previously Untreated Cancer of Unknown Primary

Inclusion Criteria * Histological confirmation of metastatic adenocarcinoma, poorly differentiated non-small cell carcinoma, or poorly differentiated squamous carcinoma * Adequate FFPE tissue or re-biopsy planned after registration but prior to treatment * Measurable disease as defined; for patients having only lesions measuring at least 1 cm to =\< 2 cm must use spiral computed tomography (CT) imaging for both pre- and post-treatment tumor assessments; disease that has received prior radiation (performed for palliative reasons) cannot be used for measurable disease * Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 * Hemoglobin (Hgb) \>= 9.0 g/dL * Absolute neutrophil count (ANC) \>= 1,500/uL * Platelet count \>= 100,000/uL * Total bilirubin =\< upper limits of normal (ULN); if liver metastases are present, total bilirubin =\< 2 x ULN * Aspartate aminotransferase (AST) =\< 2.5 x ULN; if liver metastases are present, AST =\< 5 x ULN * Creatinine =\< 1.25 x ULN; if \> 1.25 x ULN calculated creatinine clearance must be \>= 60 ml/min * Negative pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only * Provide informed written consent * Willingness to return to NCCTG enrolling institution for follow-up * Willingness to abstain from eating grapefruit or drinking grapefruit juice for the duration of the study Exclusion Criteria * Any of the following: * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception; note: adequate contraception must be used throughout the trial and for 8 weeks after the last dose of RAD001, by both sexes * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens * History of any of the following: * Known to be human immunodeficiency virus (HIV) positive * Known prior/current history of hepatitis related to hepatitis B or hepatitis C * Uncontrolled intercurrent illness including, but not limited to the following: * Ongoing or active infection (acute or chronic) * Symptomatic congestive heart failure * Unstable angina pectoris * Cardiac arrhythmia * Severely impaired lung function * Uncontrolled diabetes as defined by fasting serum glucose \> 1.5 x ULN (note: optimal glycemic control should be achieved before starting trial therapy) * Liver disease such as cirrhosis or severe hepatic impairment * Psychiatric illness/social situations that would limit compliance with study requirements * Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm =\< 4 weeks prior to registration * Other active malignancy =\< 5 years prior to registration; EXCEPTIONS: non-melanotic skin cancer or carcinoma-in-situ of the cervix; NOTE: if there is a history of prior malignancy, they must not be receiving other specific treatment for their cancer * Untreated brain metastases; NOTE: patients with treated, stable brain metastases for at least 12 weeks prior to study entry are eligible for enrollment * Impairment of gastrointestinal function or gastrointestinal disease that may significantly alter the absorption of RAD001 (e.g., ulcerative disease, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome or small bowel resection) * Active, bleeding diathesis * Receiving chronic, systemic treatment with corticosteroids or another immunosuppressive agent; topical or inhaled corticosteroids are allowed * Currently on enzyme inducing anti-convulsants (EIACs) or other strong inducers or strong inhibitors of cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4) * Current use of warfarin (Coumadin); EXCEPTION: current use of low-molecular weight heparin is allowed * Known to be HIV positive * Inoculated with live attenuated vaccines =\< 2 weeks prior to registration; note: close contact with those who have received attenuated live vaccines should be avoided during treatment with everolimus; examples of live vaccines include intranasal influenza, measles, mumps, rubella, oral polio, Bacillus Calmette-Guerin (BCG), yellow fever, varicella and TY21a typhoid vaccines * =\< 4 weeks from major surgery; note: for this study, diagnostic laparoscopy (without other intervention) and/or biopsies (needle aspirate, core biopsy, open biopsy, etc.) are not considered major surgery