This phase I trial studies the side effects and best dose of everolimus when given together with anakinra or denosumab in treating participants with cancers that have spread to other places in the body and have come back or aren't responding to treatment. Everolimus may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Anakinra is designated to block a protein that is involved in tumor development, new blood vessels growing, and the spread of cancer. Monoclonal antibodies, such as denosumab, may interfere with the ability of tumor cells to grow and spread. Giving everolimus and anakinra or denosumab may work better in treating participants with advanced cancers.

PRIMARY OBJECTIVES:

I. To determine the maximum tolerated dose (MTD) and dose-limiting toxicities (DLT) of anakinra or denosumab in combination with everolimus in patients with advanced cancers who progressed on standard therapy.

SECONDARY OBJECTIVES:

I. Preliminary assessment of antitumor efficacy of anakinra or denosumab in combination with everolimus in patients with advanced cancers.

II. Assessment of the pharmacokinetic (PK) profile of anakinra or denosumab in combination with everolimus.

III. Preliminary assessment of biomarkers.

OUTLINE: This is a dose-escalation study of everolimus. Participants are assigned to 1 of 2 arms.

ARM I: Participants receive everolimus orally (PO) daily and anakinra subcutaneously (SC) daily on days 1-28. Treatment repeats every 28 days in absence of disease progression or unacceptable toxicity.

ARM II: Participants receive everolimus PO daily on days 1-28 and denosumab SC on day 1. Treatment repeats every 28 days in absence of disease progression or unacceptable toxicity.

After completion of study treatment, participants are followed up at 30 days.

Inclusion Criteria:

• Patients with advanced or metastatic cancers that are refractory to standard therapy, relapsed after standard therapy, or who have no standard therapy available that improves survival by at least three months.
• Patients must be >= 3 weeks beyond treatment with a cytotoxic chemotherapy regimen, or therapeutic radiation, or major surgery. Patients may have received palliative localized radiation immediately before or during treatment provided that radiation is not delivered to the only site of disease being treated under this protocol. For biologic/targeted agents patients must be >= 5 half-lives or >= 3 weeks form the last dose (whichever comes first).
• Eastern Cooperative Oncology Group (ECOG) performance status =< 2.
• Absolute neutrophil count (ANC) >= 1,000/mL.
• Platelets >= 75,000/mL.
• Creatinine clearance >= 35 ml/min.
• Total bilirubin =< 2 X upper limit of normal (ULN) (exceptions may apply to benign non-malignant indirect hyperbilirubinemia such as Gilbert syndrome). Exception for patients with liver metastasis: total bilirubin =< 3 x ULN.
• Alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) and or aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT]) =< 5 X ULN. Exception for patients with liver metastasis: ALT (SGPT) =< 8 X ULN.
• Fasting lipid profile: cholesterol =< 350 mg/dL.
• Fasting lipid profile: triglycerides =< 400 mg/dL.
• Corrected calcium >= 8.4 mg/dL.
• Phosphorus >= 2.5 mg/dL for denosumab.
• Oral examination and appropriate preventive dentistry will be performed prior to the initiation of denosumab therapy.
• Negative tuberculosis quantiferon test for anakinra arm.
• Negative serology for histoplasma, blastomycosis, and Coccidioidomycosis for anakinra arm.
• Negative serology for active hepatitis B and C for anakinra arm. Patients with positive serology for hepatitis B might eligible if they are willing to take lamivudine preventive therapy.
• Women of childbearing potential and men 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 for 30 days after the last dose.
• Patients must be able to understand and be willing to sign a written informed consent document.

Exclusion Criteria:

• Uncontrolled intercurrent illness, including, but not limited to, uncontrolled infection, uncontrolled asthma, need for hemodialysis, need for ventilatory support. Treatment of pre-existing invasive fungal infections must be completed prior to starting treatment.
• Patients with an active infection.
• Pregnant or lactating women.
• History of hypersensitivity to anakinra.
• History of hypersensitivity to denosumab.
• History of hypersensitivity to everolimus.
• History of hypersensitivity to any component of the formulation.
• Patients unwilling or unable to sign informed consent document.
• Patients treated with TNF antagonists.
• Patients with a history of active systemic fungal infection.
• Patients with liver disease Child Pugh classification B and C.