Inclusion Criteria:

        All cohorts:

          -  Provision of signed and dated, written informed consent form ICF in accordance with
             International Council on Harmonization-Good Clinical Practice (ICH-GCP)and local
             legislation prior to any trial-specific procedures, sampling, or analyses.

          -  Male or female ≥18 years old at the time of signature of the ICF.

          -  ECOG performance status of 0 or 1.

          -  Life expectancy of at least 12 weeks after the start of the treatment according to the
             Investigator's judgement.

          -  Patients with radiologically documented disease progression or relapse during or after
             all standard of care treatments. Patients who are not eligible to receive standard of
             care treatments, and for whom no proven treatments exist, are eligible.

          -  Previous treatment with an anti-PD-1/PD-L1 mAb is allowed as long as the last
             administration of the anti-PD-1/PD-L1 mAb on the previous treatment occurred a minimum
             of 28 days prior to the first administration of study treatment.

          -  Patient must be willing to submit to the blood sampling for the Pharmacokinetics (PK),
             Pharmacodynamics (PD), biomarker, and PGx analyses.

          -  Adequate organ function defined as all of the following (all screening labs should be
             performed locally within 10 days of treatment initiation):

               -  Hematological

                    -  Absolute neutrophil count - ≥1.5 x 10^9/L

                    -  Platelets - ≥125 x 10^9/L

                    -  Hemoglobin 0 ≥9.0 g/dL or ≥5.6 mmol/L (red blood cell transfusion allowed to
                       meet eligibility criteria)

               -  Hepatic

                    -  Total bilirubin ≤ upper limit of normal (ULN), (patients with Gilbert's
                       syndrome, total bilirubin must be < 2 x ULN)

                    -  Aspartate Transaminase (AST) and Alanine Aminotransferase (ALT) ≤2.5 x ULN
                       OR ≤5 x ULN for patients with liver metastases

               -  Renal

                  --- Creatinine - ≤1.5 x ULN - Patients may enter if creatinine is >1.5 x ULN and
                  estimated glomerular filtration rate (eGFR) >30 mL/min/1.73 m^2 (assessed by
                  Chronic Kidney Disease Epidemiology [CKDEPI] Collaboration equation);
                  confirmation of eGFR is only required when creatinine is >1.5 X ULN

               -  Coagulation --- International Normalised Ratio (INR) or Prothrombin Time (PT).
                  Activated Partial Thromboplastin Time (aPTT) - ≤1.5 x institutional ULN. Patients
                  taking low dose warfarin must have their INR followed closely and according to
                  institutional guidelines

          -  Women of childbearing potential (WOCBP, defined as female patients who are
             premenopausal or who had no cessation of menses within 12 months without an
             alternative medical cause, but not including female patients who are permanently
             sterilized) and men able to father a child must be ready and able to use two medically
             acceptable 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 beginning at screening,
             during trial participation and until 35 days and 3 months, respectively for women and
             men, after trial completion (i.e. after the last administration of trial medication).
             A list of contraception methods meeting these criteria is provided in the patient
             information.

        Phase Ia (dose escalation part):

          -  Patients with a confirmed diagnosis of unresectable, advanced and/or metastatic solid
             tumors (any type) irrespective of the TP53 mutation status,

          -  Patient with either evaluable or non-evaluable disease.

          -  Availability and willingness to provide a sample of archival Formalin-fixed paraffin
             embedded (FFPE) tumor tissue material

        Phase Ia (Expansion Cohort):

          -  Patients with MDM2 amplified tumors and absence of known TP53 mutation

          -  At least one target lesion that can be accurately measured per RECIST 1.1. In patients
             who only have one target lesion, the baseline imaging must be performed at least two
             weeks after any biopsy of the target lesion.

        Phase Ib (expansion part):

          -  At least one target lesion that can be accurately measured per RECIST 1.1. In patients
             who only have one target lesion, the baseline imaging must be performed at least two
             weeks after any biopsy of the target lesion.

          -  Expansion cohorts:

               -  Cohort 1: Patients with unresectable, advanced and/or metastatic TP53 wt NSCLC,
                  who received in the advanced/metastatic setting, at least one line of systemic
                  medical treatment that includes, but is not limited to, a platinum-based
                  combination chemotherapy and immune checkpoint inhibitor(s) except anti-LAG-3.
                  Patients with NSCLC harboring genomic aberrations for which FDA approved targeted
                  therapy is available such as non-resistant EGFR mutations, EGFR T790M mutation,
                  ALK rearrangement, ROS re-arrangement, and BRAF V600E mutation, must have
                  received prior treatment with FDA-approved targeted therapy.

               -  Cohort 2: Patients with unresectable, advanced and/or metastatic TP53 wt
                  melanoma, who received in the advanced/metastatic setting, at least one line of
                  systemic medical treatment that has included immune checkpoint inhibitor(s),
                  except anti-LAG-3, and for patients with a V600 BRAF mutation, a prior treatment
                  with BRAF and MEK inhibitors.

               -  Cohort 3: Patients with unresectable, advanced and/or metastatic TP53 wt
                  well-differentiated or dedifferentiated liposarcoma (n = 10 patients) or TP53 wt
                  undifferentiated pleomorphic sarcoma (n = 10 patients), who received in the
                  advanced/metastatic setting, at least one line of systemic medical treatment that
                  may have included immune checkpoint inhibitor(s), except anti-LAG-3 antibody.

               -  Cohort 4: Patients with unresectable, advanced and/or metastatic TP53 wt
                  hepatocellular carcinoma (HCC), who received at least one line of systemic
                  medical treatment in the advanced/metastatic setting, with or without prior
                  treatment with anti-PD-1/PD-L1 antibody, and whose Child-Pugh score is 7 or less.

        Exclusion criteria:

          -  Previous administration of BI 907828 or any other MDM2-p53 or MDMX (MDM4)-p53
             antagonist

          -  In Phase Ib (expansion phase) only: a documented amino-acid altering mutation in TP53
             occurring in the patient's tumor.

          -  Active or untreated brain metastases. Note: Patients with previously treated brain
             metastases may participate provided they are stable, without evidence of progression
             by imaging (using the identical imaging modality for each assessment, either MRI or
             computed tomography (CT) scan), for at least four weeks prior to the first dose of
             trial treatment, and any neurologic symptoms have returned to baseline; have no
             evidence of new or enlarging brain metastases. Patients on corticosteroids must have a
             stable dose for at least 5 days prior to baseline MRI.

          -  Current use of warfarin, factor Xa inhibitors and direct thrombin inhibitors. Note:
             Low molecular weight heparin and prophylactic low dose warfarin are permitted; PT/PTT
             must meet the inclusion criteria; patients taking low dose warfarin must have their
             INR followed closely and according to institutional guidelines.

          -  Patients with history of bleeding diathesis.

          -  Major surgery (major according to the Investigator's assessment) performed within 12
             weeks prior to start of study treatment, or planned within 12 months after screening
             (e.g. hip replacement).

          -  Any other documented active or suspected malignancy or history of malignancy within 3
             years prior to screening, except appropriately treated basal cell carcinoma of the
             skin or in situ carcinoma of uterine cervix, or other local tumors 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.

          -  Currently enrolled in another investigational device or drug trial, or less than 4
             weeks since receiving other investigational treatments. Patients who are in
             follow-up/observation for another clinical trial are eligible.

          -  Patients who have been treated with any other anticancer drug within 4 weeks or within
             5 half-life periods (whichever come earlier) prior to first administration of study
             treatment.

          -  Persistent toxicity from previous treatments that has not resolved to ≤ Common
             Terminology Criteria for Adverse Events (CTCAE) Grade 1 (except for alopecia and CTCAE
             Grade 2 neuropathy, or asthenia/fatigue).

          -  Known history of human immunodeficiency virus (HIV) infection

          -  Any of the following laboratory evidence of hepatitis virus infection:

               -  Positive results of hepatitis B surface (HBs) antigen

               -  Presence of HBc antibody together with HBV-DNA

               -  Presence of hepatitis C RNA However, in Phase Ib Cohort 4 (HCC), patients with
                  HBV and/or HCV infection are allowed. Patients in Cohort 4 (HCC), with HBV
                  infection must be receiving effective antiviral therapy (viral load <100 IU/mL).

          -  Known hypersensitivity to the trial drugs or their excipients.

          -  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 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 patient or unlikely to complete the trial.

          -  Women who are pregnant, nursing, or who plan to become pregnant while in the trial;
             female patients who do not agree to the interruption of breast feeding from the start
             of study treatment to within 30 days after the last study treatment.

          -  History (including current) of interstitial lung disease or pneumonitis within the
             last 5 years.

          -  History of severe hypersensitivity reactions to other monoclonal antibodies

          -  Immunosuppressive corticosteroid doses (>10 mg prednisone daily or equivalent) within
             4 weeks prior to the first dose of study treatment.

          -  Active autoimmune disease or a documented history of autoimmune disease, except
             vitiligo or resolved childhood asthma/atopy

          -  Active infection requiring systemic treatment (antibacterial, antiviral, or antifungal
             therapy) at start of treatment in this trial.

          -  Any of the following cardiac criteria:

               -  Mean resting corrected QT interval (QTc) >470 msec

               -  Any clinically important abnormalities (as assessed by the Investigator) in
                  rhythm, conduction, or morphology of resting ECGs, e.g., complete left bundle
                  branch block, third degree heart block

               -  Any factor that increases 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 known to prolong the QT interval

               -  Patients with an ejection fraction (EF) <50% or the lower limit of normal of the
                  institutional standard will be excluded. 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,
                  multi-gated acquisition scan). 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.