BACKGROUND: Trastuzumab deruxtecan is a HER2-directed antibody-drug conjugate approved by the US Food and Drug Administration and the European Medicines Agency for HER2-mutant non-small-cell lung cancer. Few treatment options exist for patients with HER2-mutant solid tumours beyond lung cancers. We investigated trastuzumab deruxtecan in metastatic solid tumours with specific activating HER2 mutations. METHODS: In this open-label, phase 2, basket study done in 29 centres in Asia, Europe, and North America, we investigated trastuzumab deruxtecan (5·4 mg/kg every 3 weeks by intravenous infusion) in patients aged 18 years or older with unresectable or metastatic solid tumours with specific activating HER2 mutations, an Eastern Cooperative Oncology Group performance status of 0 or 1, and disease progression following previous treatment (previous HER2-targeted therapy was permitted) or with no satisfactory alternative treatment options. The primary endpoint was confirmed objective response rate by independent central review. Anti-tumour activity and safety were analysed in all patients who received at least one dose of trastuzumab deruxtecan. This trial is registered with ClinicalTrials.gov, NCT04639219, and is active but no longer recruiting. FINDINGS: Between Dec 30, 2020, and Jan 25, 2023, 102 patients (62 [61%] female and 40 [39%] male; median age 66·5 years [IQR 58-72]; 51 [50%] White, two [2%] Black or African American, 38 [37%] Asian, and 11 [11%] did not have race information reported) with solid tumours with activating HER2 mutations received trastuzumab deruxtecan and were included in the anti-tumour activity and safety analyses sets. Patients had a median of three (IQR 2-4) previous treatment regimens. The median duration of follow-up was 8·61 months (IQR 3·71-12·68). The objective response rate by independent central review was 29·4% (95% CI 20·8-39·3; 30 of 102 patients). 52 (51%) patients had a treatment-emergent adverse event of grade 3 or worse; the most common events (in ≥5% of patients) were anaemia (16 [16%]) and neutrophil count decreased (eight [8%]). Drug-related treatment-emergent serious adverse events occurred in ten (10%) patients. Adjudicated drug-related interstitial lung disease or pneumonitis of any grade occurred in 11 patients (11%; three grade 1, five grade 2, one grade 3, and two grade 5); there were two (2%) cases of fatal adjudicated drug-related interstitial lung disease or pneumonitis. INTERPRETATION: Trastuzumab deruxtecan showed anti-tumour activity and durable responses in heavily pretreated patients across multiple tumour types with activating HER2 mutations, with no new safety signals. Prespecified HER2 mutations might be targeted by HER2-directed antibody-drug conjugates and our findings support further investigation of trastuzumab deruxtecan in the pan-tumour setting. FUNDING: AstraZeneca and Daiichi Sankyo.