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

Dasatinib is designed to block certain proteins from causing cancer cells to grow out of control. This may cause the cancer cells to die.

Crizotinib is designed to block certain abnormal genes found in cancer cells. This may cause the cancer cells to die.

This is an investigational study. Dasatinib is FDA approved and commercially available for the treatment of leukemia. Crizotinib is FDA approved and commercially available for the treatment of lung cancer. The combination of dasatinib and crizotinib is currently being used for research purposes only.

Up to 176 participants will take part in this study. All will be enrolled at MD Anderson

Study Groups:

Dose Escalation Group:

If you are found to be eligible to take part in this study, you will be assigned to a either Arm A or Arm B based when you joined this study, the disease type, and the drugs you have taken in the past. Up to 5 dose levels of the study drug will be tested in each arm. Up to 6 participants will be enrolled in each dose level of arms A and B. The first group of participants in Arm A will receive the FDA approved dose of crizotinib plus the lowest dose level of dasatinib. The first group of participants in Arm B will receive the FDA approved dose of dasatinib plus the lowest dose level of crizotinib. Each new group will receive a higher dose of the study drug combination than the group before it, if no intolerable side effects were seen. This will continue until the highest tolerable dose of the study drug combination is found.

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

Dose Expansion Group:

After the highest tolerable dose level of the study drug combination for each arm is found, up to 10 additional participants will be enrolled in the dose expansion group and will receive the highest dose of the study drug combination that was tolerated in the dose escalation group.

Study Drug Administration:

Each study cycle is 28 days.

All participants will take dasatinib by mouth 1 time each day. You will take this drug alone on Day 1 of Cycle 1, before the first day you receive the study drug combination.

Then starting on Day 2 of Cycle 1, you will begin taking crizotinib by mouth 1 time daily, 1 time every other day, or 2 times daily depending on the dose level of the study drug you are assigned to. You should take dasatinib and crizotinib at least 1 hour before meals.

Study Visits:

You will have study visits on Days 1 and 15 of Cycle 1, and again before you begin each new cycle (once every 28 days). At each study visit, you will be asked about any drugs you may be taking and any side effects you may be having.

Blood/Tumor Samples and Imaging Scans

If you are in the dose expansion group:

• On Day 1 of each cycle, blood (about 1 teaspoon) will be drawn for pharmacodynamic (PD) testing before your take the first dose of study drug. PD testing measures how the level of study drug in your body may affect the disease.
• If you are one of the first ten patients enrolled in your cohort, you will take Dasatinib only on your first day of treatment (Day -1 of Cycle 1). On Day -1 and on Day 1 of Cycle 1, blood (about ½ teaspoon each time) will be drawn for pharmacokinetic (PK) testing before you take the drug and 1, 2, 4, and 8 hours after you take the drug. PK testing measures the amount of study drug in the body at different time points.
• If you are one of the first ten patients enrolled in your cohort, on Day 1 of Cycle 3 and beyond, blood (about ½ teaspoon) will be drawn for PK testing before you take the study drug.
• If you are one of the first 10 patients enrolled in your cohort, you will have a biopsy at screening and after Cycle 1. The type of biopsy you have will be based on the type of disease you have. The procedure, and its risks, will be discussed with you in more detail.

All study participants:

• On Week 3 of Cycle 1, blood (about 1 teaspoon) and urine will be collected for routine tests.
• On Day 28 of each cycle, 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 a bone scan to check the status of the disease. The actual type of scan you have will depend on what types of scans were taken at screening.
• 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 no longer be able to take the study drugs if intolerable side effects occur or if you are unable to follow study directions. If the disease gets worse, you may be eligible to continue taking the study drug. The study doctor will discuss this with you.

Your participation on the study will be over after 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 and the following tests and procedures performed:

• Your medical history will be recorded.
• You will have a physical exam, including measurement of your weight and vital signs.
• Your performance status will be recorded.
• You will be asked about any drugs you may be taking and side effects you may be having.
• 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.

Inclusion Criteria:

1. Patients must have histologically confirmed solid malignancy that is metastatic or unresectable or lymphoma, for which standard curative or palliative measures that improve survival by at least three months do not exist or are no longer effective. For the purpose of this study patients with leukemia are not eligible.
2. Age >/= 16 years.
3. Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status </= 2.
4. Patients must have normal organ and marrow function as followed defined: ANC >/= 1,000/mcL; Plt >/=75,000/mcL; total bilirubin </=2.0 mg/dL; AST (TGO)/ALT (TGP) </=2.5x upper limit of normal; if liver metastasis are present, then </= 5.0x upper limit; estimated creatinine clearance by Cockcroft-Gault equation > 30 mL/min
5. The effects of Dasatinib and Crizotinib on the developing human fetus are unknown. For this reason women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation.
6. Patients receiving palliative radiation will be eligible after a wash-out period of 2 weeks between finishing radiation and initiation of study drugs. Palliative radiation will not be allowed during cycle 1 of treatment but is permitted in this study during following cycles as long as there are evaluable lesions that are not being irradiated
7. Signed informed consent approved by the Institutional Review Board prior to patient entry.
8. Expanded cohort only: Cohort 1: patients with predominant metastatic bone disease; Cohort 2: patients with primary squamous head and neck cancers; Cohort 3: patients presenting any molecular abnormality of interest, which can include an ALK translocation, ALK amplification, ALK mutation and overexpression as determined by FISH, IHC, qPCR, qRT-PCR, array Comparative Genomic Hybridization or direct sequencing (aCGH); a c-MET abnormality, either c-MET amplification by FISH, overexpression by IHC or c-MET mutation; BRAF, DDR2 and CDKN2A mutations; and, finally, TRIM 16 expression and CCN2 expression.

Exclusion Criteria:

1. Patient receiving any concurrent chemotherapy.
2. Concurrent severe and/or uncontrolled medical disease including, but not limited to, ongoing or active infection requiring intravenous antibiotics.
3. Symptomatic congestive heart failure (NYHA Class III or IV), or unstable angina pectoris.
4. Presence of symptomatic pleural and/or pericardial effusion not appropriated treated.
5. Prolonged QTc interval (>/=500 msec), as calculated by Bazett's formula.
6. Psychiatric problems of sufficient severity to limit full compliance with the study or expose patients to undue risk.
7. Known anaphylactic or severe hypersensitivity to Dasatinib or Crizotinib or their analogs.
8. Patient has failed to recover from any prior surgery within 4 weeks of study entry.
9. Patient is pregnant or lactating. Pregnant women are excluded from this study because dasatinib and crizotinib are agents with the potential for teratogenic or abortifacient effects (Pregnancy category D).
10. Patient has had any treatment specific for tumor control within 3 weeks of dosing with investigational drugs and cytotoxic agents, or within 2 weeks of cytotoxic agent given weekly, or within 6 weeks of nitrosoureas or mitomycin C, or within 5 half-lives of biological targeted agents.
11. Patient is not able to swallow oral medication.
12. Patients receiving any medications or substances that are strong inhibitors or inducers of CYP3A4 complex are ineligible.
13. Patients with known pulmonary hypertension.