A Study to Test Different Doses of BI 891065 Alone and in Combination With BI 754091 in Asian Patients With Different Types of Advanced Cancer (Solid Tumours)

Inclusion criteria: * Of legal age (according to local legislation) at screening. No upper limit. * Signed and dated written informed consent in accordance with International Council on Harmonisation (ICH) Good Clinical Practice (GCP) and local legislation prior to admission to the trial. * Male or female patients. Women of childbearing potential (WOCBP) and men able to father a child must be ready and able to use highly effective methods of birth control per ICH M3 (R2) that result in a low failure rate of less than 1% per year when used consistently and correctly, starting with the screening visit and through 6 months after the last dose of study treatment. A list of contraception methods meeting these criteria is provided in the patient information. The requirement of contraception does not apply to women of no childbearing potential and men not able to father a child, but they must have an evidence of such at screening. * Eastern Cooperative Oncology Group (ECOG) performance status: 0 to 1 * Patients with a confirmed diagnosis of advanced, unresectable and/or metastatic solid tumours, who have failed standard treatment, or for whom no therapy of proven efficacy exists, or who are not amenable to standard therapies. * Presence of at least one measureable lesion according to Response Evaluation Criteria In Solid Tumours (RECIST) 1.1. * Life expectancy of at least 12 weeks after the start of the treatment according to the Investigator's judgement * For Part B: Patients must have at least 1 tumour lesion amenable to biopsy, and must be willing to undergo a biopsy prior to first treatment and after 3 weeks while on therapy. * For Part B: Patients with following cancer types: bladder, colon, breast, NSCLC, ovarian, pancreatic, renal, esophagogastric, sarcoma, prostate, and melanoma Exclusion criteria: * Major surgeries (major according to the Investigator's assessment) performed within 12 weeks prior to the first administration or planned within 12 months after screening (e.g., hip replacement), or moderate surgeries (moderate according to the Investigator's assessment) performed within 4 weeks prior to the first administration. * Presence of active invasive cancers other than the one treated in this trial within 5 years prior to screening, except for appropriately treated basal cell carcinoma of the skin, or in situ carcinoma of uterine cervix, or other local tumours considered cured by local treatment * Patients who must or wish to continue the intake of restricted medications or any drug considered likely to interfere with the safe conduct of the trial * Previous administration of BI 891065 or other Second Mitochondrial Activator of Caspases (SMAC) mimetic/IAP inhibitor * Patients who have been treated with any other anticancer drug or investigational drug, within 4 weeks or within 5 half-life periods (whichever is shorter) prior to first administration of BI 891065 * Persistent toxicity from previous treatments that has not resolved to ≤ Grade 1 (except for alopecia and Grade 2 neuropathy due to previous treatments) * Active, known or suspected autoimmune disease except vitiligo or resolved asthma/atopy * (Part B only) Patients removed from previous anti-Programmed-cell-death-protein-1 (PD-1) or anti-Programmed-cell-death ligand-1 (PD-L1) therapy because of a severe immune-related adverse event (irAE) * History (including current) of interstitial lung disease or pneumonitis within 5 years * Any of the following cardiac criteria: * Mean resting corrected QT interval (QTcF) \>480 msec * Any clinically important abnormalities (as assessed by the investigator) in rhythm, conduction, or morphology of resting Electrocardiograms (ECGs), e.g., complete left bundle branch block, third degree heart block * Any factors that increase the risk of QTc prolongation or risk of arrhythmic events such as heart failure, hypokalaemia, congenital long QT syndrome, family history of long QT syndrome or unexplained sudden death under 40 years-of-age, or any concomitant medication with known or possible risk of QT interval prolongation * Patients with an ejection fraction (EF) of either \<50% or less than the lower limit of normal of the institutional standard will be excluded, whichever is lower. Only in cases where the Investigator (or the treating physician or both) suspects cardiac disease with negative effect on the EF, will the EF be measured during screening using an appropriate method according to local standards to confirm eligibility (e.g., echocardiogram \[ECHO\], multi-gated acquisition scan \[MUGA\]). A historic measurement of EF no older than 6 months prior to first administration of study drug can be accepted provided that there is clinical evidence that the EF value has not worsened since this measurement in the opinion of the Investigator or of the treating physician or both * Inadequate organ function or bone marrow reserve as demonstrated by the following laboratory values: * Absolute neutrophil count (ANC) \<1.5 x 109/L (\<1500/mm\^3) * Platelet count \<100 x 10\^9/L (\<100,000/mm\^3) * Haemoglobin \<9.0 g/dL * Alanine transaminase (ALT) \>3 times the upper limit of normal (ULN) if no demonstrable liver lesion(s) (primary or metastases) or \>5 times ULN in the presence of liver lesion(s) * Aspartate aminotransferase (AST) \>3 times the ULN if no demonstrable liver lesion(s) or \>5 times ULN in the presence of liver lesion(s) * Total bilirubin \>1.5 times ULN, except for patients with Gilbert's syndrome who are excluded if total bilirubin \>3.0 times ULN or direct bilirubin \>1.5 times ULN * Serum creatinine \> 1.5 x ULN (measured by enzymatic assay, Isotope dilution mass spectroscopy \[IDMS\] standardised Jaffe assay, or non-IDMS Jaffe assay). If serum creatinine is \> 1.5 x ULN, patient is eligible if concurrent estimated glomerular filtration rate (eGFR) is ≥ 30 mL/min/1.73m\^3 (measured or calculated by Chronic Kidney Disease Epidemiology \[CKD-EPI\] formula) * Human immunodeficiency virus (HIV) infection. Test results obtained in routine diagnostics are acceptable if done within 6 months before the informed consent date. * Any of the following laboratory evidence of hepatitis virus infection. * Positive results of hepatitis B surface (HBs) antigen * Presence of hepatitis B core (HBc) antibody together with hepatitis virus B (HBV) Deoxyribonucleic acid (DNA) * Presence of hepatitis virus C (HCV) antibody together with HCV Ribonucleic acid (RNA) In Part A, test results obtained in routine clinical practice are acceptable if done within 6 months before the informed consent date. * Known relevant hypersensitivity to the trial drugs or their excipients based on the investigator's assessment * Serious concomitant disease or medical condition affecting compliance with trial requirements or which are considered relevant for the evaluation of the efficacy or safety of the trial drug, such as cardiac, neurologic, psychiatric, infectious disease or active ulcers (gastro-intestinal tract, skin) or laboratory abnormality that may increase the risk associated with trial participation or trial drug administration, and in the judgment of the Investigator would make the patient inappropriate for entry into the trial. * Chronic alcohol or drug abuse or any condition that, in the Investigator's opinion, makes them an unreliable trial patients, unlikely to complete the trial, or unable to comply with the protocol procedures * Women who are pregnant, nursing, or who plan to become pregnant during the trial. Women who are nursing can be enrolled if they stop nursing. In this case, the patient cannot resume nursing even after discontinuation of study treatment. * Untreated brain metastasis(es) that may be considered active. Patients with previously treated brain metastases may participate provided they are stable (i.e., without evidence of Progressive disease (PD) by imaging for at least 4 weeks prior to the first dose of trial treatment, and any neurologic symptoms have returned to baseline), and there is no evidence of new or enlarging brain metastases * Patients with known leptomeningeal disease * Patients receiving systemic treatment with any immunosuppressive medication within 1 week prior to treatment start (steroids of max. 10 mg/day prednisolone equivalent per day are allowed, topical and inhaled steroids are not considered as immunosuppressive).