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 requ…