An Umbrella, Modular Study Based on Epidermal Growth Factor Receptor (EGFR) Mutation Status

The goal of this screening portion of this clinical research study is to learn if you are eligible to take part in a clinical research study using Tarceva (erlotinib hydrochloride) and either Erbitux (cetuximab), Velcade (bortezomib), or Sprycel (dasatinib).

If the results of the screening portion of this clinical research study show that you are eligible to take part in one of the studies described above, the study drug that you will be assigned to take will depend on the results of biomarker analysis performed as a part of the screening tests described below. Biomarkers are chemical "markers" in the blood/tissue that may be related to how your body might react to the study drug.

Drug Administration and Study visits for Erlotinib hydrochloride:

If you will be taking Erlotinib hydrochloride in this study, you will take Erlotinib hydrochloride by mouth daily at least 1 hour before eating and 2 hours after eating. You will have study visits once a month. If you continue to be on study longer than 2 cycles, study visits may become less frequent.

At these visits, the following tests and procedures will be performed:

* Your performance status will be recorded.
* You will be asked to list any drugs you may be taking, including over-the-counter drugs.
* You will be asked about any symptoms you may have.
* You will have a physical exam, including measurement of your vital signs.
* Blood (about 2 teaspoons) will be collected for routine tests

After the first 8 weeks on study, you will have a CT or MRI scan to check the status of the disease. You will have a CT or MRI scan every 8 to 12 weeks after that.

You may continue taking Erlotinib hydrochloride for as long as you are benefitting. You will be taken off study if the disease gets worse or intolerable side effects occur. If the disease gets worse, the study doctor may assign you to 1 of 3 studies. The study doctor will discuss this in more detail with you.

Length of Study:

Your participation on this screening study will be over after all of the screening tests and procedures described above have been completed.

This is an investigational study. Up to 102 participants will take part in this study. All will be enrolled at MD Anderson.

Eligibility Criteria:
Inclusion Criteria:

1. Patients with pathologically confirmed advanced or metastatic cancer that is refractory to standard therapy, relapsed after standard therapy, or who have had no standard therapy that induces a CR rate of at least 10% or improves survival by at least three months.
2. Patients must have tumor tissue available, either from an archival specimen, or from a recent biopsy, to be analyzed for EGFR mutation. Patients must sign consent for the umbrella protocol prior testing for EGFR mutation. Patients will be eligible if they have an EGFR-sensitive mutation, OR if they have an EGFR-resistant mutation, OR if they do not have an EGFR mutation, but have benefited from EGFR inhibitor therapy (including either \>/= 4 months of stable disease \[SD\] OR a \>/= partial response \[PR\]).
3. Measurable or non-measurable disease.
4. Patients must be \>/= 6 wks beyond treatment with a nitrosourea or mitomycin-C, \>/= 4 wks beyond other chemotherapy or external beam radiation therapy (XRT), and must have recovered to \</= Grade 1 toxicity for any treatment-limiting toxicity resulting from prior therapy. (Exception: patients may have received palliative low dose XRT one week before treatment provided it is not given to the only targeted lesions).
5. (continued from above) Also, patients who have received non-chemotherapeutic biological agents will need to wait at least 5 half-lives or 4 wks, whichever is shorter, from the last day of treatment.
6. Eastern Cooperative Oncology Group (ECOG) performance status \</= 2 (Karnofsky \>/= 60%)
7. Patients must have normal organ and marrow function defined as: absolute neutrophil count \>/=1,000/mL; platelets \>/=50,000/mL; creatinine \</= 2 X upper limit of normal (ULN); total bilirubin \</= 2.0; ALT(SGPT) \</= 3 X ULN; Exception for patients with liver metastasis: total bilirubin \</= 3 x ULN; ALT(SGPT) \</= 5 X ULN.
8. Women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 30 days after the last dose.
9. Ability to understand and the willingness to sign a written informed consent document.

Exclusion Criteria:

1. Patients with uncontrolled concurrent illness, including but not limited to: ongoing or active infection; altered mental status or psychiatric illness/social situations that would limit compliance with study requirements and/or obscure study results.
2. Uncontrolled systemic vascular hypertension (systolic blood pressure \> 140 mm Hg, diastolic blood pressure \> 90 mm Hg on medication).
3. Patients with clinically significant cardiovascular disease: history of CVA within 6 months, myocardial infarction or unstable angina within 6 months, or unstable angina pectoris.
4. Patients with colorectal carcinoma with tumors that demonstrate a Kirsten rat sarcoma (KRAS) mutation.
5. Pregnant or lactating women
6. Patients with a history of bone marrow transplant within the previous two years
7. Patients with a known hypersensitivity to any of the components of the drug products.
8. Patients who will be on treatment arm consisting of erlotinib and dasatinib should not be taking any drugs that are potent inhibitors or inducers of CYP34A
9. Patients unable to swallow oral medications or with pre-existing gastrointestinal disorders that might interfere with proper absorption of oral drugs.
10. Patients with major surgery within 30 days prior to entering the study.