A Study to Determine Best Tumor Response With Trastuzumab Emtansine in Human Epidermal Growth Factor Receptor 2 (HER2) Overexpressing Solid Tumors

Inclusion Criteria: * Histologically centrally confirmed HER2-positive (immunohistochemistry \[IHC\]3+ in greater than or equal to \[\>/=\] 30 percent \[%\] of tumor cells): locally advanced (unresectable and not treatable with curative intent), or metastatic UBC or locally advanced (unresectable and not treatable with curative intent) or metastatic pancreatic cancer/cholangiocarcinoma * There must be no standard treatment options available for participants with the above HER2 overexpressing tumors and they must have undergone at least one prior platinum-based treatment for locally advanced (unresectable and not treatable with curative intent) or metastatic tumor (Note: for pancreatic cancer/cholangiocarcinoma, prior treatments are not required to be platinum-based.) * Participant's lesion should be measurable according to RECIST V1.1 on diagnostic computed tomography (CT) scan/magnetic resonance imaging (MRI); Target lesion(s) should not have been previously irradiated * At least one formalin-fixed paraffin-embedded (FFPE) biopsy of the primary tumor and/or from a metastatic site is required * Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0-2 * No significant cardiac history and a current left ventricular ejection fraction (LVEF) \>/=50% * Adequate organ function * Life expectancy of at least 12 weeks Exclusion Criteria: * Participants with previous exposure to HER2-targeted therapies in any setting * Participants showing histologically confirmed focal HER2-expression, that is, less than (\<) 30% of positively stained tumor cells * Participants with brain metastasis as the sole site of metastatic disease and/or are symptomatic or require therapy to control symptoms * Current uncontrolled hypertension (systolic greater than \[\>\] 150 millimeters of mercury \[mmHg\] and/or diastolic \>100 mmHg) * Current unstable angina pectoris * History of symptomatic congestive heart failure (CHF) of any New York Heart Association (NYHA) criteria or ventricular arrhythmia that requires treatment * History of myocardial infarction within the last 6 months * Peripheral neuropathy, Grade \>/=3 * Current dyspnea at rest due to complications of advanced malignancy, or other diseases that require continuous oxygen therapy * Current severe, uncontrolled systemic disease * History of other malignancy within the last 5 years * Concurrent, serious, uncontrolled infections or current known infection with human immunodeficiency virus (HIV), active hepatitis B and/or hepatitis C * Known prior severe hypersensitivity to trastuzumab and trastuzumab emtansine or the excipients of the investigational medicinal product (IMP) * Clinically significant bleeding within 30 days before enrollment * Major surgical procedure or significant traumatic injury within 28 days prior to randomization or anticipation of the need for major surgery during the course of study treatment * Concurrent participation in any other therapeutic clinical trial