Everolimus and Anakinra or Denosumab in Treating Participants With Relapsed or Refractory 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.