A Targeted Phase I/II Trial of ZD6474 (Vandetanib; ZACTIMA) Plus the Proteasome Inhibitor, Bortezomib (Velcade ), in Adults With Solid Tumors With a Focus on Hereditary or Sporadic, Locally Advanced or Metastatic Medullary Thyroid Cancer (MTC)

-INCLUSION CRITERIA: 1. Pathologic confirmation of cancer by the Laboratory of Pathology, National Cancer Institute (NCI) 2. Phase I: Diagnosis of recurrent, metastatic or primary unresectable solid tumor that does not have curative standard treatment. Phase II: Diagnosis of recurrent, metastatic or primary unresectable medullary thyroid cancer (MTC). 3. Measurable disease at presentation: Either by Response Evaluation Criteria in Solid Tumors (RECIST) or by measurement of serum markers (calcitonin, carcinoembryonic antigen (CEA), prostate specific antigen (PSA) or cancer antigen 125 or carbohydrate antigen 125 (CA-125) in the dose-finding portion of the study; with disease measurable by RECIST required only in the phase II cohort. 4. A life expectancy of at least 3 months and Eastern Cooperative Oncology Group (ECOG) performance status 0 1. 5. Age greater than or equal to 18 years 6. Last dose of chemotherapy or experimental therapy more than 4 weeks (6 weeks in the case of nitrosourea) prior to enrollment date; unless the last therapy consisted of an oral agent whose average half life is known to be less than 48 hours in which case only 2 weeks need to have elapsed. Regardless of the therapy, any toxicity greater than Common Terminology Criteria in Adverse Events (CTCAE) grade 1 from previous anti-cancer therapy must have been resolved. 7. Last radiotherapy treatment 4 weeks prior to starting treatment with this protocol with the exception of palliative radiotherapy and there must be sites of measurable disease that did not receive radiation. 8. Organ and marrow function as defined: * total bilirubin less than 1.5 times the upper limit of reference range (ULRR), unless the patient meets the criteria for Gilbert's Syndrome * alanine aminotransferase (ALT), aspartate aminotransferase (AST) and alkaline phosphatase (ALP) all three less than 2.5 times the upper limit of the reference range (ULRR), or less than 5 times the ULRR if judged by the investigator to be related to liver metastases * serum creatinine less than 1.5 times the ULRR or creatinine clearance greater than or equal to 30 mL/minute (calculated by Cockcroft-Gault formula or measured in a timed urine collection) * serum calcium below the CTCAE grade 1 upper limit (11.5mg/dL or 2.9 mmol/L). In cases where the serum calcium is below the normal range, the calcium adjusted for albumin is calculated and substituted for the measured value. * serum potassium greater than the lower limit of normal (LLN) and less than 5.5 mmol/L. * serum magnesium greater than the LLN and less than 3.0 mg/dL or 1.23 mmol/L. * absolute neutrophil count greater than or equal to 1000/mm(3) * platelet count greater than or equal to 100,000/mm(3) * Prothrombin time (PT) less than or equal to 4 seconds above ULN and partial thromboplastin time (PTT) less than or equal to 10 seconds above ULN. 9. Ability to understand and sign an informed consent document. 10. Provision of informed consent prior to any study-related procedures 11. Negative pregnancy test for women of childbearing potential 12. Ability and willingness to follow the guidelines of the clinical protocol including visits to National Cancer Institute (NCI), Bethesda, Maryland for treatment and follow up visits. 13. Because the effects of chemotherapy on the developing human fetus are potentially harmful, female patients must be one year post-menopausal, surgically sterile, or using an acceptable method of contraception during and continued after the last dose of study medications (oral contraceptives, barrier methods, approved contraceptive implant, long-term injectable contraception, intrauterine device or tubal ligation). Male patients must be surgically sterile or using an acceptable method of contraception during their participation in this study. Contraceptive use will continue for at least four months after the last dose of study medication. EXCLUSION CRITERIA: 1. Patients with cancer potentially curable by surgical excision alone or patients who have not received therapy that might be considered standard and potentially curable. 2. Evidence of severe or uncontrolled systemic disease or any concurrent condition including, but not limited to symptomatic congestive heart failure, unstable angina pectoris, unstable hypertension, seizure disorder, or psychiatric illness which in the Investigators opinion makes it undesirable for the patient to participate in the trial or which would jeopardize compliance with the protocol. 3. Untreated brain metastases (or local treatment of brain metastases within the last 6 months) due to the poor prognosis of these patients and difficulty ascertaining the cause of neurologic toxicities. 4. During Phase II enrollment: Prior therapy with vandetanib. 5. Women who are currently pregnant or breast-feeding, due to the possible adverse effects on the developing fetus and infants. 6. The presence of a second malignancy within the last 2 years, other than squamous cell carcinoma of the skin or in situ cervical cancer because it will complicate the primary objective of the study. Cancer survivors who have been free of disease for at least two years can be enrolled in this study. \- There is one other exception to the exclusion of secondary malignancies: multiple endocrine neoplasia type 2 (MEN2) patients with concurrent medullary thyroid cancer and pheochromocytoma may be enrolled at the discretion of the Principal Investigator. 7. Patients with evidence of a bleeding diathesis that cannot be corrected with standard therapy or factor replacement. 8. Any unresolved toxicity greater than CTCAE grade 1 (except alopecia) from previous anticancer therapy. Patients with grade 1 neuropathy will be evaluated on a case by case basis for entry into study. Baseline conditions will be taken into consideration. 9. Major surgery within 4 weeks, or incompletely healed surgical incision before starting study therapy. 10. Clinically significant cardiovascular event (e.g. myocardial infarction, superior vena cava syndrome (SVC), New York Heart Association (NYHA) classification of heart disease greater than or equal to 2 within 3 months before entry; or presence of cardiac disease that, in the opinion of the Investigator, increases the risk of ventricular arrhythmia. 11. History of arrhythmia (multifocal premature ventricular contractions PVCs, bigeminy, trigeminy, ventricular tachycardia, or uncontrolled atrial fibrillation) which is symptomatic or requires treatment (CTCAE grade 3) or asymptomatic sustained ventricular tachycardia. Atrial fibrillation controlled on medication is not excluded. 12. History (within the last 6 months) or presence of stroke/cerebrovascular accident. 13. Corrected QT interval (QTc) prolongation with other medications. If the medication can be discontinued and an alternative medication started that does not cause QTc prolongation, the patient would be eligible. If no alternative medication is available and the medication cannot be discontinued for medical reasons, then the patient would not be eligible. 14. Congenital long Q wave, T wave (QT) syndrome, or 1st degree relative with unexplained sudden death under 40 years of age. 15. Presence of left bundle branch block (LBBB). 16. QTc with Bazett's correction that is not measurable, or greater than or equal to 480 msec on screening electrocardiogram (ECG). (Note: If a patient has a QTc interval greater than or equal to 480 msec on screening ECG, the screen ECG may be repeated twice (at least 24 hours apart). The average QTc from the three screening ECGs must be less than 480 msec in order for the patient to be eligible for the study). Patients who are receiving a drug that has a risk of QTc prolongation are excluded if QTc is greater than or equal to 460 msec. 17. Concurrent medication that may cause QTc prolongation or induce Torsades de Pointes: Those medications in Group One will not be allowed. Those medications in Group Two will be allowed. 18. Hypertension not controlled by medical therapy (systolic blood pressure greater than 160 mm Hg or diastolic blood pressure greater than 100 mm Hg) 19. Currently active (uncontrolled) diarrhea greater than or equal to CTCAE Grade 2 that may affect the ability of the patient to absorb the vandetanib or tolerate diarrhea. Antidiarrhea medications are allowed in patients with chronic diarrhea. 20. Concomitant medications that are potent inducers (rifampicin, rifabutin, phenytoin, carbamazepine, phenobarbital and St. John's Wort) of cytochrome P450 3A4 (CYP3A4) function. 21. Major surgery within 4-weeks, or incompletely healed surgical incision before starting study medications. Biopsies, port placements, and dental work are examples of acceptable (nonmajor) surgery within the 4 week time frame. 22. Inability to take oral medications for whatever reason.