The goal of this clinical research study is to find the highest tolerable dose of the combinations of pazopanib and either lapatinib or trastuzumab that can be given to patients with advanced cancer. The safety of the drug combinations will also be studied.

Pazopanib is designed to block the growth of blood vessels that supply nutrients needed for tumor growth. This may prevent or slow the growth of cancer cells.

Lapatinib is designed to prevent or slow down the growth of cancer cells by blocking 2 proteins on the surface of the cancer cell, which are HER 1 and HER 2 receptors.

Trastuzumab is designed to prevent or slow down the growth of cancer cells by blocking proteins inside the cancer cell, called the Her2/neu receptor.

Study Groups:

If you are found to be eligible to take part in this study, your doctor will decide which study drugs you will receive based on the disease type and the drugs you have taken in the past

You will receive either a combination of pazopanib and lapatinib (Arm A) or a combination of pazopanib and trastuzumab (Arm B).

Up to 5 dose levels of each combination will be tested. Up to 6 participants will be enrolled at each dose level of each combination. The first group of participants will receive the lowest dose level of each combination. Each new group(s) will receive a higher combination than the group before it, if no intolerable side effects were seen. Participants may be enrolled on 1-3 similar dose levels at the same time. You will be assigned to a dose level based on when you joined this study. This will continue until the highest tolerable dose(s) of the study drug combination is found.

The dose of the study drug combination that you receive may be lowered if you have intolerable side effects.

Once the highest tolerable doses of the different combinations are found, this dose of each combination will be given to an expansion group of 20 extra participants.

Study Drug Administration:

If you are in Arm A, you will take lapatinib by mouth 1 time each day. You will take pazopanib by mouth 1 time every other day (Day 1, 3, 5, and so on). You should take pazopanib and lapatinib either 1 hour before or 2 hours after eating a meal.

If you are in Arm B, you will take pazopanib by mouth 1 time each day. You will receive trastuzumab by vein on Days 1, 8, 15, and 22 of each cycle. The first infusion will be over 90 minutes. If you handle the infusion well, the next infusions will be over 30 minutes. You should take pazopanib either 1 hour before or 2 hours after eating a meal.

Each study cycle is 28 days.

Study Visits:

At all study visits, you will be asked about any drugs you may be taking and side effects you may be having.

Week 3 of Cycle 1, blood (about 1 teaspoon) and urine will be collected for routine tests.

During Week 3 of Cycles 2 and beyond, blood (about 1 teaspoon) will be drawn for routine tests.

During Week 4 of Cycle 2 and then every 2-3 cycles:

• You will have a CT scan, MRI scan, PET scan, and/or x-ray to check the status of the disease.
• If the study doctor thinks it is needed, blood (about 1 teaspoon) will be drawn to measure tumor markers.

Length of Study:

You may continue taking the study drugs for as long as the doctor thinks it is in your best interest. You will be taken off study early if the disease gets worse, if you continue to have intolerable side effects, or if you are unable to follow study directions.

Your participation on the study will be over once you have completed the end-of-study visit.

End-of-Study Visit:

Within 30 days after your last dose of study drugs, you will have an end-of-study visit. At this visit, the following tests and procedures performed:

• Your medical history will be recorded.
• You will have a physical exam.
• You will be asked about any drugs you may be taking and side effects you may be having.
• Your weight, vital signs, and performance status will be recorded.
• Blood (about 2 teaspoons) and urine will be collected for routine tests.
• If the study doctor thinks it is needed, blood (about 1 teaspoon) will be drawn to measure tumor markers.
• If the study doctor thinks it is needed, you will have a chest x-ray, CT scan, MRI scan, and/or PET scan to check the status of the disease.

This is an investigational study. Pazopanib is FDA approved and commercially available for the treatment of renal cell carcinoma. Lapatinib and trastuzumab are FDA approved and commercially available for the treatment of breast cancer. The combination of pazopanib and lapatinib or pazopanib and trastuzumab is investigational.

Up to 174 participants will take part in this study. All will be enrolled at MD Anderson.

Inclusion Criteria:

1. 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.
2. Patients must have measurable or evaluable disease.
3. Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status </= 2.
4. Abnormal organ function is permitted; however, patients must have : Plt >/=100,000/, absolute neutrophil count (ANC) >/=1500, total Bilirubin </=2.0 mg/dl, Creatinine </=2.0 mg/dl and Prothrombin Time/International Normalized Ratio/Partial Thromboplastin Time (PT/INR/PTT) within 1.5 X upper limit of normal (ULN).
5. A woman is eligible to enter and participate in the study if she is of non-childbearing potential (i.e., physiologically incapable of becoming pregnant), including any female who has had a hysterectomy, bilateral oophorectomy (ovariectomy), bilateral tubal ligation, is post-menopausal (total cessation of menses for ≥ 1 year); OR if of childbearing potential, has a negative serum pregnancy test at screening, and agrees to use adequate contraception.
6. A man with a female partner of childbearing potential is eligible to enter and participate in the study if he uses a barrier method of contraception or abstinence during the study.
7. Signed informed consent approved by the Institutional Review Board prior to patient entry.
8. Expanded Cohort only: Patients must have HER2 amplification, HER2 mutation, c-Met amplification, c-Met mutation, EML4-ALK translocation, or epidermal growth factor receptor (EGFR) mutation.

Exclusion Criteria:

1. Poorly-controlled hypertension (systolic blood pressure [SBP] >/= 140 mmHg, or diastolic blood pressure [DBP]>/= 90 mmHg).
2. Concurrent severe and/or uncontrolled medical disease (e.g. uncontrolled diabetes,congestive cardiac failure )
3. History of myocardial infarction, admission for unstable angina, cardiac angioplasty or stenting within three months of Day 1 of treatment period.
4. History of venous or arterial thrombosis within 3 months of Day 1 of treatment Period.
5. Current use of therapeutic warfarin. NOTE: both low molecular weight heparin and prophylactic low-dose warfarin are permitted; however, PT/PTT must meet above inclusion criteria.
6. Excessive risk of bleeding or thrombosis as defined by stroke or severe bleeding within the prior 6 months.
7. Patients who received investigational drugs, chemotherapy or immunotherapy patient must be >/= five half-lives or >/= 3 weeks from the last dose of treatment, whichever is shorter.
8. Any major surgery or radiotherapy within 14 days of treatment.
9. Patients with a documented Left Ventricular Ejection Fraction < 45%.