A Study to Test How Well Different Doses of BI 3706674 Are Tolerated by People With Advanced Cancer in the Stomach and Oesophagus

Inclusion Criteria:

1. Patients with pathologically confirmed diagnosis of locally advanced or metastatic gastric adenocarcinoma (GAC), oesophageal adenocarcinomas (EAC), and gastroesophageal junction adenocarcinoma (GEJAC) with Kirsten rat sarcoma viral oncogene homolog (KRAS) wild type (wt) amplification and documented disease progression despite at least 1 line of prior therapy. KRAS status will be confirmed retrospectively for those with a known KRAS status or determined prospectively (dose confirmation and expansion) if KRAS status is unknown, using archival tissue (if available) or a fresh biopsy.

   Dose escalation (Part A) only: Patients with advanced or metastatic relapsed or refractory solid tumours of any histology with KRAS wt amplification or harbouring a KRAS G12V mutation who have exhausted treatment options known to prolong survival for their disease. Detection of KRAS status by a local test is allowed for enrolment but will be retrospectively confirmed.
2. Patients who have failed conventional treatment or for whom no therapy of proven efficacy exists or who are not eligible for established treatment options.
3. Dose confirmation (Part B) only: Patient is willing and able to undergo mandatory pre- and on-treatment low risk tumour biopsies. Patients with a high risk for biopsy complications can be included without undergoing pre- and on-treatment tumour biopsy as long as archival tumour tissue is available for confirmation of KRAS status.
4. At least one target lesion that can be measured per RECIST version 1.1 (radiated lesions do not qualify as target lesions unless there has been demonstrated progression of the lesion after completion of radiotherapy) Dose escalation (Part A) only: Patients with no lesions measurable per RECIST version 1.1 may be included if agreed between Sponsor and investigator.
5. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.
6. All toxicities related to previous anti-cancer therapies have resolved ≤ CTCAE Grade 1 prior to trial treatment administration (except for alopecia and peripheral neuropathy which must be ≤ CTCAE Grade 2 and amenorrhea/menstrual disorders which can be any grade).
7. Life expectancy ≥3 months at the start of treatment in the opinion of the investigator.
8. Age ≥18 years of age, or over the legal age of consent as required by local legislation.

Further inclusion criteria apply.

Exclusion Criteria:

1. Previous anti-cancer chemotherapy within 3 weeks of the first administration of trial drug.
2. Previous anti-cancer hormonal treatment or anti-cancer immunotherapy within 2 weeks of the first administration of trial drug.
3. Previous treatment with rat sarcoma (RAS), mitogen-activated protein kinases (MAPKs) or son of sevenless homolog 1 (SOS1) targeting agents.
4. Presence of cardiovascular abnormalities such as uncontrolled hypertension (defined as systolic blood pressure ≥140 and/or diastolic blood pressure ≥90 millimetre of mercury (mmHg)), congestive heart failure New York Heart Association (NYHA) classification of ≥ III or IV, unstable angina or poorly controlled arrhythmia. History of myocardial infarction, stroke, or pulmonary embolism within 6 months prior to randomisation.
5. Left ventricular ejection fraction (LVEF) \<50%.
6. Congenital or family history of long QT prolongation syndrome.
7. Mean resting corrected QT interval (QTcF) \>470 msec.
8. Radiotherapy within 2 weeks prior to start of treatment, except as follows:

   * Palliative radiotherapy to regions other than the chest is allowed if completed at least 2 weeks prior to randomisation.
   * Single dose palliative radiotherapy for symptomatic metastasis within 2 weeks prior to randomisation may be allowed but must be discussed with the Sponsor.

Further exclusion criteria apply.