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).