Ceritinib and Everolimus in Treating Patients With Locally Advanced or Metastatic Solid Tumors or Stage IIIB-IV Non-small Cell Lung Cancer

Inclusion Criteria:

* For dose escalation cohort: patients with histologically or cytologically confirmed locally advanced or metastatic solid tumors who have failed at least one line of therapy
* For dose expansion cohort: patients with stage IIIB or IV ALK + NSCLC who have failed at least one line of therapy and are progressing on an ALK inhibitor; for dose expansion, patients who have ROS1 rearrangement testing by either next generation sequencing (NGS) or fluorescence in situ hybridization (FISH) will be eligible
* Absolute neutrophil count (ANC) \>= 1,500/microliter
* Platelets \>= 100,000/microliter
* Hemoglobin (Hgb) \>= 9 g/dL
* Creatinine =\< 1.5 x upper limit of normal (ULN)
* Prothrombin time (PT), partial thromboplastin time (PTT) =\< 1.5 x ULN
* Total bilirubin =\< 1.5 x ULN
* Alanine transaminase (ALT) and aspartate aminotransferase (AST) \< 1.5 x ULN (\< 5 x ULN if patient has liver metastasis)
* Patient will have a tumor suitable for fine needle aspirates (FNA) or core biopsy for research purposes (2 or more FNAs if core is not feasible)
* Able to swallow oral medications
* Patient must have performance status =\< 2 on the Eastern Cooperative Oncology Group (ECOG) performance scale
* Measurable disease by RECIST or evaluable disease (e.g., bone metastasis, or lesions which do not fulfill RECIST criteria for metastatic disease)
* ALK-positive NSCLC patients with asymptomatic central nervous system (CNS) metastases who are neurologically stable or have not required increasing doses of steroids within the 2 week prior to study entry to manage CNS symptoms
* Non-ALK-positive NSCLC patients with CNS metastasis should have completed a course of therapy would be eligible for the study provided they are clinically stable for 1 month prior to entry as defined as: (1) no evidence of new or enlarging CNS metastasis (2) off steroids
* Negative serum or urine pregnancy test beta-human chorionic gonadotropin (beta hCG) within 2 weeks prior to receiving the first dose of study medication for women of childbearing age
* Patient must have completed any systemic therapy regimens (except an ALK inhibitor) and therapeutic radiation a minimum of 21 days prior to initiation of study therapy
* Fasting serum cholesterol =\< 300 mg/dL OR =\< 7.75 mmol/L AND fasting triglycerides =\< 2.5 x ULN; NOTE: in case one or both of these thresholds are exceeded, the patient can only be included after initiation of appropriate lipid lowering medication
* Signed informed consent obtained prior to any screening procedures

Exclusion Criteria:

* Patients who have received prior everolimus or ceritinib
* Patients with known history of extensive disseminated bilateral interstitial fibrosis or interstitial lung disease, including a history of pneumonitis, hypersensitivity pneumonitis, interstitial pneumonia, obliterative bronchiolitis, and clinically significant radiation pneumonitis (i.e. affecting activities of daily living or requiring therapeutic intervention)
* Patients currently receiving anticancer therapies or who have received anticancer therapies within 4 weeks including chemotherapy, radiation therapy, antibody based therapy, etc.
* Known intolerance or hypersensitivity to everolimus or other rapamycin analogs (e.g. sirolimus, temsirolimus)
* Patients with known hypersensitivity to any of the excipients of ceritinib (microcrystalline cellulose, mannitol, crospovidone, colloidal silicon dioxide and magnesium stearate)
* Known impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of oral everolimus
* Uncontrolled diabetes mellitus as defined by hemoglobin A1c (HbA1c) \> 8% despite adequate therapy; patients with a known history of impaired fasting glucose or diabetes mellitus (DM) may be included, however blood glucose and antidiabetic treatment must be monitored closely throughout the trial and adjusted as necessary
* Patient has clinically significant, uncontrolled heart disease and/or recent cardiac event (within 6 months), such as:

  * Unstable angina within 6 months prior to screening
  * Myocardial infarction within 6 months prior to screening
  * History of documented congestive heart failure (New York Heart Association functional classification III-IV)
  * Uncontrolled hypertension defined by a systolic blood pressure (SBP) \>= 160 mmHg and/or diastolic blood pressure (DBP) \>= 100 mmHg, with or without antihypertensive medication - initiation or adjustment of antihypertensive medication(s) is allowed prior to screening
  * Ventricular arrhythmias; supraventricular and nodal arrhythmias not controlled with medication
  * Other cardiac arrhythmia not controlled with medication
  * Corrected QT interval (QTc) \> 450 msec using Fridericia correction on the screening electrocardiogram (ECG)
* Patients who have any severe and/or uncontrolled medical conditions such as:

  * Active (acute or chronic) or uncontrolled severe infection, liver disease such as cirrhosis, decompensated liver disease, and chronic hepatitis (i.e. quantifiable hepatitis B virus test \[hepatitis B virus (HBV)-deoxyribonucleic acid (DNA)\] and/or positive hepatitis B surface antigen \[HbsAg\], quantifiable hepatitis C virus test \[hepatitis C virus (HCV)-ribonucleic acid (RNA)\])
  * Known severely impaired lung function (spirometry and carbon monoxide diffusing capacity \[DLCO\] 50% or less of normal and oxygen \[O2\] saturation 88% or less at rest on room air)
  * Active, bleeding diathesis
* Chronic treatment with high dose corticosteroids or other immunosuppressive agents; topical, inhaled, and low dose oral corticosteroids are allowed provided stable dosing for at least 2 weeks
* Receiving medications that meet one of the following criteria and that cannot be discontinued at least 1 week prior to the start of treatment with ceritinib and for the duration of the study participation:

  * Medication with a known risk of prolonging the QT interval or inducing Torsades de Pointes
  * Strong inhibitors or strong inducers of cytochrome P450, family 3, subfamily A, polypeptide 4/cytochrome P450, family 3, subfamily A, polypeptide 5 (CYP3A4/5)
  * Medications with a low therapeutic index that are primarily metabolized by CYP3A4/5, cytochrome P450, family 2, subfamily C, polypeptide 8 (CYP2C8) and/or cytochrome P450, family 2, subfamily C, polypeptide 9 (CYP2C9)
  * Therapeutic doses of warfarin sodium (Coumadin) or any other Coumadin-derived anti-coagulant; anticoagulants not derived from warfarin are allowed (e.g., dabigatran, rivaroxaban, apixaban)
  * Unstable or increasing doses of corticosteroids
  * Enzyme-inducing anticonvulsive agents
  * Herbal supplements
* Known history of human immunodeficiency virus (HIV) seropositivity
* Patients who have received live attenuated vaccines within 1 week of start of everolimus and during the study; patient should also avoid close contact with others who have received live attenuated vaccines; examples of live attenuated vaccines include intranasal influenza, measles, mumps, rubella, oral polio, Bacillus Calmette-Guerin (BCG), yellow fever, varicella and TY21a typhoid vaccines
* Patients who have a history of another primary malignancy unless the patient has been disease free for \>= 3 years
* Patients with a history of non-compliance to medical regimens or who are considered potentially unreliable or will not be able to complete the entire study
* Patients who are currently part of or have participated in any clinical investigation with an investigational drug within 1 month prior to dosing (except ALK inhibitors)
* Pregnant or nursing (lactating) women, where pregnancy is defined as the state of a female after conception and until the termination of gestation, confirmed by a positive hCG laboratory test
* Women of child-bearing potential (WOCBP), defined as all women physiologically capable of becoming pregnant, unless they are using highly effective methods of contraception during dosing and for 3 months after the last dose of study treatment; highly effective contraception methods include:

  * Total abstinence (when this is in line with the preferred and usual lifestyle of the subject; periodic abstinence (e.g., calendar, ovulation, symptothermal, post-ovulation methods) and withdrawal are not acceptable methods of contraception
  * Female sterilization (have had surgical bilateral oophorectomy with or without hysterectomy) or tubal ligation at least six weeks before taking study treatment; in case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment
  * Male sterilization (at least 6 months prior to screening) with the appropriate post-vasectomy documentation of the absence of sperm in the ejaculate; for female subjects on the study the vasectomized male partner should be the sole partner for that subject
  * Combination of any two of the following:

    * Use of oral, injected or implanted hormonal methods of contraception or other forms of hormonal contraception that have comparable efficacy (failure rate \< 1%), for example hormone vaginal ring or transdermal hormone contraception
    * Placement of an intrauterine device (IUD) or intrauterine system (IUS)
    * Barrier methods of contraception: condom or occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/vaginal suppository; in case of use of oral contraception, women should have been stable on the same pill for a minimum of 3 months before taking study treatment; women are considered post-menopausal and not of child bearing potential if they have had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical profile (e.g., age appropriate, history of vasomotor symptoms) or have had surgical bilateral oophorectomy (with or without hysterectomy) or tubal ligation at least six weeks prior to screening; in the case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment is she considered not of child bearing potential
* Sexually active males unless they use a condom during intercourse while taking drug and for 3 months after the last dose of study treatment; male patients for 3 months should not father a child in this period; a condom is required to be used also by vasectomized men in order to prevent delivery of the drug via seminal fluid; also male patients whose sexual partner(s) are WOCBP who are not willing to use adequate contraception during the study and for 3 months after the end of enrollment