Inclusion Criteria:

- Histologically confirmed solid malignancy meeting 1 of the following criteria:

- Non-small cell lung cancer

- Head and neck squamous cell carcinoma

- Non-gastroesophageal junction esophageal cancer

- Solid tumor that is sensitive to carboplatin and/or taxanes including, but not
limited to, any of the following (dose-escalation phase only):

- Salivary gland cancer

- Gastric cancer

- Breast cancer

- Ovarian cancer

- Anal cancer

- No Kaposi sarcoma

- Metastatic or unresectable disease and considered incurable

- Known HIV infection by ELISA, positive western blot, or any other federally approved
(licensed) HIV test

- Measurable disease

- At least 1 measurable tumor

- No known brain metastases

- Hormone receptor status not specified

- Menopausal status not specified

- ECOG performance status (PS) 0-2 (Karnofsky PS 50-100%)

- Life expectancy > 12 months

- WBC ≥ 3,000/mm³

- ANC ≥ 1,500/mm³

- Platelet count ≥ 100,000/mm³

- Total bilirubin normal

- AST and ALT ≤ 2.5 times upper limit of normal

- Creatinine normal OR creatinine clearance ≥ 50 mL/min

- Serum magnesium normal

- Serum potassium normal

- CD4 count > 150/mm³ within the past 2 weeks

- Not pregnant or nursing

- Negative pregnancy test

- Fertile patients must use adequate contraception (hormonal or barrier method of birth
control, or abstinence) prior to, during, and for ≥ 3 months after study completion

- Must be capable of complying with study protocol

- No history of allergic reactions attributed to compounds of similar chemical or
biologic composition to vorinostat or other agents used in study (including
hypersensitivity to paclitaxel, Cremophor, or platinum-based therapy)

- Able to take oral medication (vorinostat tablets must be swallowed whole)

- No peripheral neuropathy > grade 1

- No uncontrolled intercurrent illness including, but not limited to, any of the
following:

- Ongoing or active infection

- Opportunistic infection

- Symptomatic congestive heart failure

- Unstable angina pectoris

- Cardiac arrhythmia

- Psychiatric illness and/or social situations that would limit compliance with
study requirements

- Recovered to ≤ grade 1 toxicities

- No more than 1 prior systemic therapy for palliative treatment of metastatic or
unresectable relapsed disease

- At least 4 weeks since prior chemotherapy or radiotherapy (6 weeks for nitrosoureas
or mitomycin C) given with curative intent

- Prior taxane, including paclitaxel or docetaxel, and/or platinum exposure allowed
provided patients did not experience disease progression within 3 months after the
platinum-based therapy

- Any prior or concurrent antiretroviral therapy allowed provided patient has been on a
stable regimen for ≥ 4 weeks with no intention to change the regimen within 8 weeks
after study entry

- No concurrent zidovudine or stavudine

- No prior vorinostat or other known HDAC inhibitors as cancer therapy

- At least 2 weeks since prior valproic acid

- No other concurrent investigational agents

- No concurrent ketoconazole