The goal of this clinical research study is to find the highest tolerable dose of the combination of erlotinib and pralatrexate that can be given to patients with advanced cancer. The safety of the drug combination will also be studied.

Pralatrexate is designed to block the body's ability to make folic acid, a protein that may help cancer tissue to develop and spread.

Erlotinib hydrochloride is designed to block proteins that are thought to cause cancer cells to grow. Erlotinib may help slow the growth of tumors.

Study Groups:

If you are found to be eligible to take part in this study, you will be assigned to a dose level of erlotinib and pralatrexate based on when you join this study.

Dose Escalation:

Several dose levels of erlotinib and pralatrexate will be tested. Three (3) to 6 participants will start at the lowest planned doses of erlotinib and pralatrexate. Each new group of 3-6 participants will receive a higher dose than the group before it, if no intolerable side effects were seen. This will continue until the highest tolerable dose of erlotinib in combination with pralatrexate is found.

Dose Expansion:

Once the highest tolerable dose or most appropriate combination dose level is found, 10 more participants will take the study drugs at this dose level.

Study Drug Administration:

Each study cycle is 28 days.

Up to 10 days before you start treatment , you will start taking folic acid to help lower the risk of side effects. Although the study drug is designed to prevent the body from making folic acid that could help cancer grow and spread, some folic acid is needed to prevent side effects in non-cancerous tissue. You will take folic acid by mouth 1 time every day during treatment and for at least 30 days after you received the last dose of pralatrexate.

Up to 10 days before you start treatment, you will receive a vitamin B12 injection. You will receive an injection of Vitamin B12 about every 3 months after that.

On Days 1, 8, and 15 of each cycle, you will receive pralatrexate by vein over 3-5 minutes.

You will take erlotinib hydrochloride by mouth 1 time a day every day. You should take erlotinib hydrochloride on an empty stomach either 1 hour before eating or 2 hours after eating.

You will take erlotinib at home except on the days when you have a study visit. You should take it at about the same time each day with about a cup (8 ounces) of water.

Study Visits:

At every study visit, you will be asked about any current health conditions you have, any other drugs you are taking, and if you have had any side effects.

If the screening tests were performed within 7 days before Cycle 1, tests and procedures may not have to be repeated.

At any time during Cycle 1:

• You will have a physical exam, including measurement of your weight at least 1 time per cycle.
• Your vital signs will be measured.
• Your performance status will be recorded.
• Blood (about 2 teaspoons) will be drawn for routine tests and to see how well your blood clots.
• If you are taking part in the expansion phase, blood (about 2 teaspoons) will be drawn for pharmacodynamic (PD) testing.

At any time during Cycle 2:

• You will have a physical exam, including measurement of your weight at least 1 time per cycle.
• Your vital signs will be measured.
• Your performance status will be recorded.
• Blood (about 4 teaspoons) will be drawn for routine tests.
• If you are taking part in the expansion phase, blood (about 2 teaspoons) will be drawn for PD testing.

About every 8 weeks, you will have an x-ray, CT scan, MRI scan, and/or positron emission computed tomography (PET)/CT scan to check the status of the disease. Blood (about 1 teaspoon) may be drawn for tumor marker testing depending on the type of tumor. If the study doctor thinks it is needed, they will be performed more or less often.

At any time during Cycle 3 and beyond:

• You will have a physical exam, including measurement of your weight at least 1 time per cycle.
• Your vital signs will be measured.
• Your performance status will be recorded.
• Blood (about 2 teaspoons) will be drawn for routine tests.

Length of Dosing:

You may continue taking the study drugs for as long as the doctor thinks it is in your best interest. You will no longer be able to take the study drugs if the disease gets worse, if intolerable side effects occur, or if you are unable to follow study directions.

Your participation on the study will be over once you have completed the end-of-treatment and follow-up visits.

End of Dosing Visit:

After you are finished taking the study drugs:

• You will have a physical exam, including measurement of your weight and vital signs.
• Your performance status will be recorded.
• Blood (about 2 teaspoons) and urine will be collected for routine tests.

This is an investigational study. Pralatrexate is FDA approved and commercially available for the treatment of cutaneous T-cell lymphoma (CTCL) and peripheral T-cell lymphoma (PTCL). Erlotinib is FDA approved and commercially available for the treatment of pancreatic cancer and non small cell lung cancer (NSCLC). The study drug combination is investigational.

Up to 74 patients will take part in this study. All will be enrolled at MD Anderson.

Inclusion Criteria:

1. Measurable or non-measurable disease.
2. Patients with advanced cancer should be refractory to standard therapy, relapsed after standard therapy, or have no standard therapy that improves survival by at least three months.
3. Patients must be at least 3 weeks after cytotoxic therapy and at least 5 half lives after their previous treatment or 3 weeks, whichever shorter, after biologic therapy. Patients may receive palliative radiotherapy immediately before or during treatment provided that not all target lesions are radiated.
4. Eastern Cooperative Oncology Group (ECOG) performance status </= 2 (Karnofsky >/= 60%).
5. Patients must have normal organ and marrow function defined as: absolute neutrophil count >/=1,000/mL; platelets >/=100,000/mL; creatinine < 2.0; total bilirubin < 2.0; ALT(SGPT) </=3 X upper limit of normal (ULN); Exception for patients with liver metastasis: ALT(SGPT) </= 5 X ULN.
6. 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.
7. Ability to understand and the willingness to sign a written informed consent document.
8. For the MTD expansion cohort, patients will be eligible if they meet one of the following criteria: I. Have an epidermal growth factor receptor (EGFR)-sensitive mutation (as G719C in exon 18, E746-A750 in exon 90, L858R in exon 21) and have been previously treated with EGFR inhibitor therapy but have subsequently developed resistance, OR II. Have an EGFR-resistant mutation (as T790M in exon 20), OR III. 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]).
9. Age >/= 12 years

Exclusion Criteria:

1. Patients with uncontrolled concurrent illness, including but not limited to: ongoing or active infection requiring hospitalization; psychiatric illness/social situations that would limit compliance with study requirements.
2. Exclusion of patients with creatinine >2.0 and bilirubin > 2.0.
3. Patients with colorectal carcinoma with tumors that demonstrate a Kirsten rat sarcoma (KRAS) mutation.
4. Pregnant or lactating women.
5. Patients with a history of bone marrow transplant within the previous two years.
6. Patients with a known hypersensitivity to any of the components of the drug products.
7. Patients with major surgery within 30 days prior to entering the study.