Tivantinib and Temsirolimus in Treating Patients With Solid Tumors That is Metastatic or Cannot be Removed by Surgery

Inclusion Criteria: * Patients must have histologically confirmed solid malignancy (excluding lymphoma) that is metastatic or unresectable and for which standard curative or palliative systemic therapies (such as chemotherapy, targeted therapies or immunotherapy) do not exist or are no longer effective * Patients must have measurable or evaluable disease, as defined by Response Evaluation Criteria In Solid Tumors (RECIST) 1.1 * No prior treatment with temsirolimus or an agent specifically targeting met proto-oncogene (c-Met) * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Life expectancy of greater than 12 weeks * Hemoglobin \>= 9.0 g/dL * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin =\< 1.5 X institutional upper limit of normal * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< institutional upper limit of normal * Serum creatinine =\< institutional upper limit of normal or creatinine clearance (either estimated or calculated) \>= 60 mL/min/1.73 m for patients with creatinine levels above institutional normal * Fasting glucose =\< 150 mg/dL * Fasting cholesterol level \< 350 mg/dl * Fasting triglycerides =\< 300 mg/dl * Phosphorus \>= institutional lower limit of normal (repletion allowed) * Patients with treated, stable brain metastases are allowed to enroll; patients must be at least 4 weeks from radiation and off any medications used to treat brain metastases including steroids; patients are allowed to be on antiepileptic medications that are not metabolized by cytochrome P450 3A4 or 2C19; patients with brain metastases must have stable brain imaging within 4 weeks prior to starting study * Women of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation and up to 3 months after discontinuation of study drugs; men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of ARQ 197 administration; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Any of the following: * Chemotherapy =\< 3 weeks prior to entering the study (6 weeks for nitrosoureas or mitomycin C) * Radiotherapy, endocrine therapy or targeted therapy for malignancy =\< 2 weeks prior to registration * Patients who have not recovered (=\< grade 1) from adverse events due to agents administered more than 4 weeks earlier (tolerable grade 2 adverse events may be allowed at the discretion of the investigator; diarrhea must be grade 1 or lower without the scheduled use of antidiarrheal medications) * Prior anticancer therapy with an mammalian target of rapamycin (mTOR) inhibitor (everolimus, temsirolimus, desferolimus) or agent specifically targeting c-Met * Patients who are receiving any other investigational agents * Patients may not have clinically symptomatic hypothyroidism; testing is not required for eligibility * History of allergic reactions attributed to compounds of similar chemical or biologic composition to ARQ 197 or temsirolimus * ARQ 197 is a sensitive substrate for 2C19 and 3A4, a strong inhibitor for 2C19 and moderate inhibitor by in vitro data only for 3A4; temsirolimus is a sensitive substrate for CYP 3A4 and a weak inhibitor of CYP2D6 and CYP3A4/5; per the UWinRx Drug Interaction Policy, the following medications are contraindicated or must be used with caution * Contraindicated: * CYP2C19 sensitive substrates (unless close monitoring with labs or drug levels with dose adjustments is feasible), inducers, and moderate/strong inhibitors of CYP2C19; patients taking these concurrent medications are ineligible unless they can be switched to alternative medications prior to initiation of the study * CYP3A4/5 inducers and moderate/strong inhibitors of CYP3A4/5; patients taking these concurrent medications are ineligible unless they can be switched to alternative medications prior to initiation of the study * Use with caution: * CYP2C19 non-sensitive substrates with a narrow therapeutic window and weak inhibitors are permitted if no acceptable alternatives are available as determined by the treating physician; however, caution should be used; consider monitoring with labs or drug levels and dose adjustments of the medication if feasible; other non-sensitive substrates are allowed on study * CYP3A4/5 sensitive substrates and any non-sensitive substrates with a narrow therapeutic window and weak inhibitors are permitted if no acceptable alternatives are available as determined by the treating physician; however, caution should be used; consider monitoring with labs or drug levels and dose adjustments of the medication if feasible; other non-sensitive substrates are allowed on study * CYP2D6 inducers, moderate/strong inhibitors or sensitive substrates are permitted if no acceptable alternatives are available; however, caution should be used; other non-sensitive substrates or weak inhibitors of CYP2D6 are allowed on study * History of congestive heart failure defined as class II to IV per New York Heart Association (NYHA) classification; active coronary artery disease (CAD); clinically significant bradycardia (\< 50 beats per minute \[bpm\]) or other uncontrolled, cardiac arrhythmia defined as \>= grade 3 according to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE), version 4.0, or uncontrolled hypertension (as determined by the investigator); myocardial infarction occurring within 6 months prior to study entry (myocardial infarction occurring \> 6 months prior to study entry is permitted) * Patients with uncontrolled diabetes (as determined by the investigator); well-controlled diabetic patients with fasting glucose \< 150 are eligible if they have been on stable doses of medications for diabetes for at least 4 weeks prior to study entry * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded; breastfeeding should be discontinued if the mother is treated on this study * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible * Patients with malabsorption syndrome or other condition that would interfere with intestinal absorption of pills; patients must be able to swallow pills