Inclusion Criteria:

          -  Histologically or cytologically confirmed diagnosis of an advanced, unresectable
             and/or metastatic non-haematologic malignancy. Patient must have measurable or
             evaluable lesions (according to Response Evaluation Criteria In Solid Tumors (RECIST)
             1.1).

          -  Eastern Cooperative Oncology Group score of 0 or 1

          -  Availability and patient willingness to provide a sample of tumour for confirmation of
             the patient´s Human epidermal growth factor receptor 2 (HER2) status. This sample can
             be archival material obtained at any time prior to study enrollment

          -  Patient willing to undergo a fresh tumour biopsy prior to first treatment and also 5-7
             hours (h) after any treatment with BI 1810631 during cycle 1 (except biopsies of brain
             metastases) for pharmacodynamic assessments

          -  Adequate organ function defined as all of the following:

               -  Absolute neutrophil count (ANC) ≥ 1.5 x 109/L (≥ 1.5 x 103/μL) (≥ 1500/mm3);
                  haemoglobin ≥ 9.0 g/dL (≥ 90 g/L) (≥ 5.6 mmol/L); platelets ≥ 100 x 109/L (100 x
                  103/μL) (100 x 103/mm3) without the use of hematopoietic growth factors within 4
                  weeks of start of trial medication

               -  Total bilirubin ≤ 1.5 times the upper limit of normal (ULN), except for patients
                  with Gilbert's syndrome: total bilirubin ≤ 3 x ULN or direct bilirubin ≤ 1.5 x
                  ULN

               -  Creatinine ≤ 1.5 x ULN. If creatinine is > 1.5 x ULN, patient is eligible if
                  concurrent creatinine clearance ≥ 50 ml/min (measured or calculated by Chronic
                  Kidney Disease Epidemiology (CKD-EPI) formula or Japanese version of CKD-EPI
                  formula for Japanese patients)

               -  Aspartate transaminase (AST) and alanine transaminase (ALT) ≤ 3 x ULN if no
                  demonstrable liver metastases, or otherwise ≤ 5 x ULN if transaminase elevation
                  is attributable to liver metastases

               -  Alkaline Phosphatase < 5 x ULN

          -  Recovered from any previous therapy-related toxicity to ≤ Common Terminology Criteria
             for Adverse Events (CTCAE) Grade 1 at start of treatment (except for alopecia, stable
             sensory neuropathy and hypothyroidism (patients on thyroid replacement therapy) which
             must be ≤ CTCAE Grade 2)

          -  Life expectancy of at least 12 weeks at the start of treatment in the opinion of the
             Investigator

          -  At least 18 years of age at the time of consent or over the legal age of consent in
             countries where that is greater than 18 years

          -  Signed and dated written informed consent in accordance with International Council on
             Harmonisation-Good Clinical Practice (ICH-GCP) and local legislation prior to
             admission to the trial

          -  Male or female patients. Women of childbearing potential (WOCBP)1 and men who are able
             to father a child must be ready and able to use highly effective methods of birth
             control per International Council on Harmonisation (ICH) M3 (R2) that result in a low
             failure rate of less than 1% per year when used consistently and correctly

        Additional Inclusion criteria for Phase Ia

          -  Patients with a documented diagnosis of HER2 aberration: overexpression OR gene
             amplification OR non-synonymous somatic mutation OR gene rearrangement involving HER2
             or Neuregulin 1 (NRG1)

          -  Patient who has failed conventional treatment or for whom no therapy of proven
             efficacy exists or who is not eligible for established treatment options. Patient must
             have exhausted, or not be a suitable candidate for, available treatment options known
             to prolong survival for their disease

        Additional Inclusion criteria for Phase Ib

          -  Patient with documented HER2 Exon20 insertion-mutation positive non-small cell lung
             cancer (NSCLC) as per local results

          -  Patient who had received, in the advanced/metastatic setting, at least one line of
             systemic therapy. Patients with NSCLC harboring additionally genomic aberrations for
             which approved targeted therapy is available such as but not limited to non-resistant
             epidermal growth factor receptor (EGFR) mutations, EGFR T790M mutation, Anaplastic
             lymphoma kinase (ALK) rearrangement, reactive oxygen species (ROS) re-arrangement, and
             v-raf murine sarcoma viral oncogene homolog B (BRAF) V600E mutation, must have
             received prior treatment with an approved targeted therapy

        Exclusion Criteria:

          -  Major surgery (major according to the investigator's assessment) performed within 4
             weeks prior to first trial treatment or planned within 6 months after screening

          -  Previous or concomitant malignancies other than the one treated in this trial within
             the last 2 years, except;

               -  effectively treated non-melanoma skin cancers

               -  effectively treated carcinoma in situ of the cervix

               -  effectively treated ductal carcinoma in situ

               -  other effectively treated malignancy that is considered cured by local treatment.

          -  Treatment with a systemic anti-cancer therapy or investigational drug within 21 days
             or 5 half-lives (whichever is shorter) of the first treatment with the study
             medication

          -  Patients who must or wish to continue the intake of restricted medication or any drug
             considered likely to interfere with the safe conduct of the trial

          -  Use of concomitant medications that are narrow therapeutic index drugs that are
             substrates of P-Glycoprotein (P-gp) or Breast Cancer Resistance Protein (BCRP) (e.g.
             digoxin, dabigatran etexilate)

          -  Treatment with strong Cytochrome P450 3A4 (CYP3A4) inhibitors

          -  Treatment with strong Cytochrome P450 3A (CYP3A) inducers Further exclusion criteria
             apply