In this research study, the investigators are looking to see how effective STA-9090 is in treating esophagogastric cancer. The investigators will also evaluate the side effects of STA-9090, and examine the relationship between the presence of HSP-90 and how well study participants respond to STA-9090. STA-9090 works by blocking a protein in tumor cells called HSP90, which is thought to play a role in tumor growth. By interfering with this protein's function, STA-9090 may help kill tumor cells. This drug has been used in other research studies and information from those other research studies suggests that this agent may help to slow tumor growth in esophagogastric cancer.

• Each treatment cycle lasts 4 weeks during which time the study drug will be administered for three consecutive weeks followed by 1 week of no study drug. STA-9090 will be given by intravenous infusion.
• Participants will come to the clinic on Days 1, 8, and 15 of all cycles. At these visits, the following tests and procedures will be performed: Review of current medications and any side effects experienced; Performance status evaluation; Physical examination; Vital signs; Routine blood tests; CT scan of the chest, abdomen, and pelvis (every 2 cycles) and Optional FDG-PET scan (every 2 cycles).
• Participants may remain on this research study for as long as their cancer is responding to the study drug and they are not experiencing any severe side effects.

Inclusion Criteria:

• Participants must have histologically or cytologically confirmed advanced esophageal, gastroesophageal, or gastric cancer. When possible, archived biopsy or resection specimens must be available for correlative SNaPshot and FISH studies.
• Participants must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as 20mm or greater with conventional techniques or as 10mm or greater with spiral CT scan (per RECIST criteria).
• Participants must have progressed through prior 1st-line therapy. For the purposes of this trial, neoadjuvant chemoradiation or peri-operative chemotherapy may be considered as prior 1st-line treatment in the event of metastatic recurrence.
• 18 years of age or older
• Life expectancy of greater than 12 weeks
• ECOG Performance status of 1 or greater
• Participants must have normal organ and marrow function as defined in the protocol.
• Participants must have adequate peripheral IV access. Administration of STA-9090 via indwelling catheters is prohibited at this time.
• No concurrent active primary or metastatic cancer other than superficial squamous cell or basal cell skin cancer.
• At least 3 weeks or 5 half-lives must have elapsed between the most recent dose of any prior anticancer therapy and the start date of treatment with STA-9090. Participants must have resolution to baseline of all toxicities associated with prior anticancer therapies.
• Women of child-bearing potential and men must agree to use adequate contraception prior to study entry and for the duration of study participation.

Exclusion Criteria:

• Participants may not be receiving any other standard or investigational anticancer agents, with the exception of hormonal therapy.
• Participants with known CNS metastases must have received whole-brain radiation or other appropriate therapy not less than 4 weeks prior to starting the study drug and exhibit clinical stability of brain disease.
• History of allergic reactions attributed to compounds of similar chemical or biologic composition to STA-9090 or to the excipients PEG 300 and Polysorbate 80.
• Ventricular ejection fraction of 55% or less at baseline.
• Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia other than chronic atrial fibrillation, or psychiatric illness/social situations that would limit compliance with study requirements.
• Pregnant women are excluded from this study. Breastfeeding should be discontinued
• HIV-positive individuals on combination antiretroviral therapy are ineligible.