This multicenter, open-label dose-escalation study with an extension phase will evaluate the safety and pharmacokinetics of lumretuzumab in combination with pertuzumab and paclitaxel in participants with metastatic breast cancer expressing HER3 and HER2 protein. Cohorts of participants will receive escalating doses of lumretuzumab intravenously (IV) every three weeks (Q3W) in combination with pertuzumab 840 milligrams (mg) IV initial dose followed by 420 mg IV Q3W and paclitaxel 80 milligrams per square meter (mg/m^2) IV weekly. After completion of dose-limiting toxicity period (21 days), the study will be conducted in two extension phase cohorts: Cohort 1 and Cohort 2. Enrollment in Extension Phase Cohort 2 will occur only upon completion of Extension Phase Cohort 1. Anticipated time on study treatment is until disease progression or unacceptable toxicity occurs.