The purpose of this Phase I study is to test the safety of rhuMAb 2C4 to see what effects (good and bad) it has on patients with certain types of cancer, and also to find the highest dose of rhuMAb that can be given without causing severe side effects. All study participants will be assigned to specific group to evaluate different dosages of rhuMAb 2C4. The study is scheduled to run for up to one year depending on how patients respond to the study treatment.

Inclusion Criteria:

• Signed informed consent
• Age >=18 years old
• ECOG performance status of 0 or 1 (see Appendix F)
• Life expectancy of >=12 weeks
• Histologically documented, incurable, locally advanced or metastatic solid malignancies
• Disease progression on or after standard effective therapy or a malignancy for which there is no standard therapy
• At least one bi-dimensionally measurable lesion (>=2 cm [>=1 cm on spiral CT scan])
• HER2-negative status as defined by fluorescence in situ hybridization (FISH) testing (only for subjects with breast cancer)
• Use of an effective means of contraception for women of childbearing potential
• Granulocyte count of >=1500/uL, platelet count of >=100,000/uL, and hemoglobin of >=9 g/dL
• Serum bilirubin less than or equal to the upper limit of normal (ULN) and alkaline phosphatase, AST, and ALT <=2.5x ULN (ALT and AST <=5x ULN for subjects with liver metastases; alkaline phosphatase <=5x ULN for subjects with liver or bone metastases)
• Serum creatinine less than or equal to ULN or creatinine clearance of >=60 mL/min
• International normalized ratio (INR) of <1.3 and activated partial thromboplastin time (aPTT) of <1.5x ULN

Exclusion Criteria:

• Pleural effusions, ascites, or bone lesions as the only manifestation of the current cancer
• Symptomatic or untreated brain metastases
• Prior chemotherapy, hormonal therapy (except for androgen-deprivation therapy for subjects with prostate cancer), radiotherapy, or immunotherapy within 4 weeks of Day 1 (within 6 weeks for nitrosoureas or mitomycin)
• Prior treatment with Herceptin
• Prior cumulative doxorubicin dose of >360 mg/m2 or the equivalent
• History of other malignancies within 5 years of Day 1 except for adequately treated carcinoma in situ of the cervix or basal or squamous cell skin cancer
• History of significant cardiac disease, unstable angina, congestive heart failure, myocardial infarction, or ventricular arrhythmia requiring medication
• Ejection fraction of <50% or below the lower limit of normal determined by ECHO (Subjects who are unable to have ejection fraction evaluated by ECHO may have ejection fraction evaluated by a MUGA scan, although this must be discussed with the Medical Monitor prior to enrollment.)
• Active infection requiring IV antibiotics
• Uncontrolled hypercalcemia (>11.5 mg/dL)
• Clinically important history of liver disease, including viral or other hepatitis, current alcohol abuse, or cirrhosis
• Known human immunodeficiency virus (HIV) infection
• Any other diseases, metabolic dysfunction, physical examination finding, or clinical laboratory finding giving reasonable suspicion of a disease or condition that contraindicates the use of an investigational drug or that may affect the interpretation of the results or render the subject at high risk from treatment complications
• Major surgery or significant traumatic injury within 3 weeks of Day 1
• Pregnancy or lactation
• Inability to comply with study and follow-up procedures