This randomized pilot clinical trial studies high-dose or low-dose vorinostat in combination with carboplatin or paclitaxel in treating patients with advanced solid tumors. Vorinostat may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as carboplatin and paclitaxel, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving different doses of vorinostat together with carboplatin or paclitaxel may kill more tumor cells.

PRIMARY OBJECTIVES:

I. To determine whether high dose, short course vorinostat achieves higher peak serum concentrations than standard dosing.

SECONDARY OBJECTIVES:

I. To determine the toxicity profiles of two different escalated intermittent dosing schedules of vorinostat combined with carboplatin at an area under curve (AUC) of 5.

II. To describe the response rate in patients with advanced solid tumors treated with these regimens.

III. To develop pharmacodynamic markers for vorinostat. IV. To determine the toxicity profiles of escalated intermittent dosing schedule of vorinostat at 1200 mg combined with paclitaxel at 175 mg/m^2 and to describe the response rate in patients with advanced solid tumors treated with this regimen.

OUTLINE: Patients are randomized to 1 of 4 treatment arms.

ARM I: Patients receive high-dose vorinostat orally (PO) once daily (QD) on days 1-3 and low-dose vorinostat PO QD on days 8-10 (course 1). After 5 days, patients receive high-dose vorinostat PO QD on days 1-3 and carboplatin IV over 30 minutes on day 3 of all subsequent courses.

ARM II: Patients receive high-dose vorinostat and low-dose vorinostat as in arm I. After 5 days, patients receive lower-dose vorinostat PO QD on days 1-3 and carboplatin IV over 30 minutes on day 3 of all subsequent courses.

ARM III: Patients receive low-dose vorinostat PO QD on days 1-3 and high-dose vorinostat PO QD on days 8-10 (course 0). After 5 days, patients receive vorinostat and carboplatin as in Arm I.

ARM IV: Patients receive low-dose vorinostat and high-dose vorinostat as in Arm III. After 5 days, patients receive vorinostat and carboplatin as in Arm II.

ARM V: Patients receive low-dose vorinostat PO QD on days 1-3 and mid-dose vorinostat PO QD on days 8-10 (course 0). After 5 days, patients receive mid-dose vorinostat PO QD on days 1-3 and paclitaxel IV over 3 hours on day 3.

ARM VI: Patients receive mid-dose vorinostat PO QD on days 1-3 and low-dose vorinostat PO QD on days 8-10 (course 0). After 5 days, patients receive vorinostat and paclitaxel as in Arm V.

In all arms, courses repeat every 21 days in the absence of disease progression or unacceptable toxicity.

After completion of study therapy, patients are followed up for 4 weeks.

Inclusion Criteria:

• Patients must have histologically confirmed malignancy that is metastatic or unresectable and for which no superior curative or palliative measures are known
• At least 4 weeks must have passed since prior chemotherapy or radiation therapy; 6 weeks if the last regimen included BCNU or mitomycin C
• Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1
• Life expectancy of greater than 3 months
• Leukocytes > 3,000/mcL
• Absolute neutrophil count > 1,500/mcL
• Platelets > 100,000/mcL
• Total bilirubin < institutional upper limits of normal
• Potassium < institutional upper limits 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, or < 5 x ULN if liver metastases are present
• Creatinine within normal institutional limits OR creatinine clearance > 60 mL/min/1.73 m^2 for patients with creatinine levels above institutional normal
• Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

• Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier (except alopecia, lymphopenia, hyperglycemia, hypoalbuminemia and elevated serum alkaline phosphatase); all other toxicities should have resolved to grade 1 or less prior to beginning treatment
• Patients may not be receiving any other investigational agents
• Patients with known brain metastases that are untreated or have progressed after definitive therapy should be excluded from this clinical trial; patients with treated brain metastases, who are no longer receiving steroids for at least 14 days, are not receiving enzyme-inducing anti-epileptic drugs, and have no unstable neurologic symptoms may be enrolled at the discretion and joint decision of the principal investigator and treating physician
• Prior or current use of valproic acid, a histone deacetylase (HDAC) inhibitor
• History of allergic reactions attributed to compounds of similar chemical or biologic composition to paclitaxel, vorinostat or carboplatin
• Inability to swallow oral medications
• 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
• Women that are pregnant or breastfeeding are excluded from this study; all women of child-bearing potential must have a negative pregnancy test before receiving vorinostat; women of child-bearing potential and men must agree to use adequate contraception for the duration of the study; breastfeeding should be discontinued if the mother is treated with vorinostat; these potential risks may also apply to other agents used in this study; subjects that become pregnant or think they may be pregnant while taking part in this study should notify their treating physician immediately
• Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible; appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated