A Study of MM-111 in Combination With Multiple Treatments in Patients With HER2 Positive Cancer

Inclusion Criteria * Patients must have histologically or cytologically confirmed advanced cancer that is positive for HER2, either: * At least 3+ positive by immunohistochemistry, or * Gene amplified positive by fluorescence in situ hybridization (FISH). Chromogenic in situ hybridization (CISH) is acceptable to confirm HER2 positivity if FISH results are not available. * The patient's cancer must have recurred or progressed following standard therapy or have not responded to standard therapy. (Patients with previously untreated HER2+ metastatic gastric or gastro-esophageal junction cancer can be enrolled onto the cisplatin, capecitabine, and trastuzumab + MM-111 arm of the study.) * Patients must be ≥ 18 years of age. * Patients or their legal representatives must be able to understand and sign an informed consent. * Patients should have evaluable or measurable disease ≥ 1 cm. * Patients must have ECOG PS ≤ 1 or Karnofsky performance score of ≥ 70. * Patients must have adequate hematologic status as evidenced by: * Absolute neutrophil count (ANC) ≥ 1,500 cells/mm3 * Platelet count ≥ 100,000 platelets/mm3 * Hemoglobin ≥ 9 g/dL * For arms 1, 2, 3 and 4 patients must have adequate hepatic function as evidenced by: * Serum total bilirubin ≤ 1.5 × the upper limit of normal (ULN) * Aspartate aminotransferase (AST), alanine aminotransferase (ALT), and alkaline phosphatase ≤ 2.5 x ULN (5 × ULN is acceptable if liver metastases are present) * For arm 5 (Docetaxel) patients must have adequate hepatic function as evidenced by: * Serum bilirubin within normal limits, * AST and/or ALT \< 1.5 X ULN and alkaline phosphatase \< 2.5 X ULN if concomitantly elevated * Patients must have adequate renal function as evidenced by: * Serum creatinine ≤ 1.5 × ULN * Calculated clearance 60 mL/min/1.73 m2 for patients with creatinine levels above institutional normal * Patients must be recovered from the effects of any prior surgery, radiotherapy or other antineoplastic therapy. National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE v.4.0) up to Grade 1 is acceptable for patients with pre-existing peripheral neuropathy. * Patients must have a life expectancy of at least 3 months. Women of childbearing potential as well as fertile men and their partners must agree to abstain from sexual intercourse or to use an effective form of contraception during the study and for 60 days following the last dose of MM-111. Exclusion Criteria: * Patients for whom potentially curative antineoplastic therapy is available * Patients who are pregnant or lactating * Patients with an active infection or with an unexplained fever \> 38.5°C during screening visits or on the first scheduled day of dosing. (At the discretion of the Investigator, patients with tumor fever may be enrolled.) * Patients with untreated and/or symptomatic primary or metastatic central nervous system (CNS) malignancies (Patients with CNS metastases who have undergone surgery or radiotherapy, whose disease is stable, and who have been on a stable dose of corticosteroids for at least 2 weeks prior to the first scheduled day of dosing will be eligible for the trial.) * Patients with known hypersensitivity to any of the components of MM-111 or who have had hypersensitivity reactions to fully human monoclonal antibodies. * Patients with a known history of hypersensitivity to any of the drug components of a particular regimen. * Patients who have received other recent antitumor therapy including: * Investigational therapy administered within the 28 days prior to the first scheduled day of dosing MM-111. Dosing in \< 28 days since receiving investigational therapy is acceptable once a time interval equal to at least five half-lives of the investigational agent have passed. * Any standard chemotherapy or radiation within 14 days (and having passed the time of any actual or anticipated toxicities) prior to the first scheduled dose of MM-111. There is no necessary washout for trastuzumab. Patients enrolled to the lapatinib-containing arms of the study do not need to have a washout period for lapatinib. * Patients with New York Heart Association (NYHA) Class III or IV congestive heart failure or left ventricular ejection fraction (LVEF) \< 50% * History of myocardial infarction within 12 months of enrollment * Uncontrolled hypertension (systolic blood pressure \>180 mm Hg or diastolic blood pressure \>100 mm Hg) * Known angina pectoris requiring medication * Known clinically significant valvular heart disease * Known history of high-risk arrhythmias * Known history of congestive heart failure * Lack of physical integrity of the upper gastrointestinal tract or malabsorption syndrome * Active gastrointestinal bleedingPatients who have received prior maximum cumulative anthracycline doses: * doxorubicin or liposomal doxorubicin doses \> 360 mg/m2 * mitoxantrone \> 120 mg/m2 and idarubicin \> 90 mg/m2 * epirubicin doses higher than 720 mg/m2 * Other (e.g., liposomal doxorubicin or other anthracycline equivalent of 360 mg/m2 of doxorubicin) * If more than 1 anthracycline has been used, the cumulative dose must not exceed the equivalent of 360mg/m2 of doxorubicin * Patients with a history of allogeneic transplant. (Patients with a history of autologous bone marrow or stem cell transplant may be enrolled.) * Patients with known human immunodeficiency virus (HIV), hepatitis B or C. (If patients have previously been treated for hepatitis C and have undetectable viral loads, they can be considered eligible for the trial.) * Patients with any other medical or psychological condition, deemed by the Investigator to be likely to interfere with a patient's ability to sign informed consent, cooperate and participate in the study, or interfere with the interpretation of the results