This phase I trial studies the side effects and best dose of onalespib and CDKI AT7519 in treating patients with solid tumors that have spread from the primary site (place where they started) to other places in the body (metastatic) or cannot be removed by surgery. Onalespib and CDKI AT7519 may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth.

PRIMARY OBJECTIVES:

I. To establish the safety, tolerability, and the maximum tolerated dose of the combination of onalespib and AT7519M (CDKI AT7519).

SECONDARY OBJECTIVES:

I. To determine the pharmacokinetics of the combination of onalespib and AT7519M.

II. To assess the pharmacodynamic effect of the combination of onalespib and AT7519M on HSP70 expression and modulation of HSP90 client proteins in peripheral blood mononuclear cells (PBMCs), plasma, and tumor biopsies.

III. To observe and record anti-tumor activity.

OUTLINE: This is a dose-escalation study.

Patients receive onalespib intravenously (IV) over 1 hour on days 1 and 4 (cycle 0 only). Patients then receive onalespib IV over 1 hour and CDKI AT7519 IV over 1 hour on days 1, 4, 8, and 11 (cycle 1 and subsequent cycles thereafter). Cycles repeat every 21 days (7 days for course 0 only) in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up for 30 days.

Inclusion Criteria:

• Patients must have histologically confirmed solid tumor that is metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective
• Patients must have evaluable disease or disease measurable per Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1; measurable disease is defined as at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as >= 20 mm (>= 2 cm) with conventional techniques or as >= 10 mm (>= 1 cm) with spiral computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam
• There are no limits on prior lines of therapy; however, patients must have recovered to eligibility levels from prior toxicity or adverse events as a result of previous treatment prior to entering the study (except alopecia)
• Eastern Cooperative Oncology Group (ECOG) performance status 0-1
• Life expectancy of greater than 3 months
• Absolute neutrophil count >= 1,500/microliters
• Platelets >= 100,000/microliters
• 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]) =< 2.5 X institutional upper limit of normal
• Creatinine < 1 X institutional upper limit of normal OR creatinine clearance >= 50 mL/min determined by Cockcroft-Gault formula
• Creatine phosphokinase =< institutional upper limit of normal
• The effects of onalespib and AT7519M on the developing human fetus are unknown; for this reason, women of childbearing potential and male patients with partners of childbearing potential must agree to use adequate contraception (hormonal or barrier method of birth control or abstinence) prior to study entry, for the duration of study participation, and for 2 months after completion of study; 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; women of childbearing potential enrolling on study must have a negative pregnancy test within 72 hours of enrollment in order to be eligible; because there is an unknown but potential risk to nursing infants secondary to treatment of the mother with onalespib and AT7519M, breastfeeding should be discontinued while the mother is treated with onalespib and AT7519M
• Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

• Patients who have had chemotherapy or radiotherapy within 3 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study; patients who have had prior onalespib or AT7519M as a monotherapy will not be excluded
• Patients who are receiving any other investigational agents
• Patients with known brain metastases or carcinomatous meningitis are excluded from this clinical trial, with the exception of patients with brain metastatic disease that has previously been treated and remained stable on MRI >= 2 months after treatment, without steroids or anti-epileptic medications; these patients may be enrolled at the discretion of the principal investigator
• History of allergic reactions attributed to compounds of similar chemical or biologic composition to onalespib or AT7519M
• 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; additionally, patients with other co-morbid disease or metabolic dysfunction that would render the subject at high risk for treatment complications may be excluded at the discretion of the principal investigator in the interest of patient safety
• The effects of onalespib and AT7519M on the developing human fetus are unknown; for this reason, pregnant women are excluded from this study
• Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy known to interact with CYP isoenzymes are ineligible; in addition, HIV patients with CD4 count < 200 cells/uL are ineligible; appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated
• Consistent corrected QT (QTc) > 450 msec for men and > 470 msec for women by Fridericia formula, on 3 separate electrocardiograms (ECGs); patients with a history of long QTc syndrome or personal or family history of ventricular arrhythmias will be excluded
• Patients with pre-existing retinal disease on ophthalmologic exam will be excluded due to potential eye toxicities known to be associated with onalespib
• Patients with left ventricular ejection fraction < 50% on echocardiogram or multigated acquisition scan will be excluded based on known cardiotoxicities associated with onalespib
• Patients with grade >= 2 peripheral neuropathy will not be permitted on study