A Trial to Find and Investigate a Safe Dose of a New Substance (BI 754091) for Patients With Solid Tumours

Inclusion Criteria: * Provision of signed and dated, written Informed Consent Form (ICF) prior to any trial-specific procedures, sampling, or analyses. If a patient declines to participate in the voluntary pharmacogenetics component of the trial, he/she will not be excluded from other aspects of the trial. * Patients ≥18 years of age at the time of signature of the ICF * Phase Ia (dose-escalation) * patients with a histologically confirmed diagnosis of advanced, unresectable, and/or metastatic solid tumours (any type). * patients who have received all therapy known to confer clinical benefit (including anti-PD-1 or anti-PDL1 therapies, if relevant), or for whom no therapy of proven efficacy exists, or who are not amenable to standard therapies. Patients with anti- PD-1 or anti-PDL1 experience must have a minimum of 60 days between the last dose of the previous anti PD-1/PD-L1 and Cycle 1 Day 1 of BI 754091 treatment. * Patients may agree to provide optional paired biopsies. * Phase Ib (dose expansion) * patients with a histologically confirmed diagnosis of select advanced, unresectable, and/or metastatic solid tumours with either 1) high tumor mutation excluding high microsatellite instability or 2) refractory squamous cell cervical, anal and skin tumors, or 3) recurrent vaginal or vulvar squamous cell carcinoma. * All patients must have measurable lesions according to Response Evaluation Criteria in Solid Tumours (RECIST) v1.1 must have at least 1 tumour lesion amenable to biopsy, and must be medically fit and willing to undergo a biopsy before first treatment and, unless clinically contraindicated, after 6 weeks on therapy * patients who are anti-PD-1 and anti-PDL-1naïve but have failed conventional treatment (excluding anti-PD-1 treatment), or for whom no therapy of proven efficacy exists, or who are not amenable to standard therapies. * Eastern Cooperative Oncology Group (ECOG) score: 0 to 1 * Life expectancy of at least 12 weeks after the start of the treatment according to the Investigator's judgement * Females of child-bearing potential willing to use adequate contraceptive measures from the time of screening until 6 months after trial discontinuation, who are not or will not be breast feeding, and agree to have pregnancy tests prior to the start of dosing and at regular visits during the trial. Females not of childbearing potential must have evidence of such by fulfilling one of the following criteria at screening: * Post-menopausal: defined as more than 50 years-of-age and amenorrhoeic for at least 12 months following cessation of all exogenous hormonal treatments * Documentation of irreversible surgical sterilization by hysterectomy, bilateral oophorectomy, or bilateral salpingectomy * Women under 50 years-of-age would be considered postmenopausal if they have been amenorrhoeic for at least 12 months following the cessation of exogenous hormonal treatments, and have serum follicle-stimulating hormone and luteinizing hormone levels in the postmenopausal range for the institution. * For women of childbearing potential using a contraceptive pill, an additional barrier method is necessary. Acceptable highly effective methods of contraception include total sexual abstinence when this is in line with the preferred and usual lifestyle of the study participant (periodic abstinence such as calendar, ovulation, symptothermal, post-ovulation methods and withdrawal are not acceptable methods of contraception), an intrauterine device or intrauterine hormone-releasing system, bilateral tubal ligation, and vasectomised partner (with post-vasectomy proof of absence of sperm) * Further inclusion criteria apply Exclusion criteria: * Major surgery (major according to the Investigator's assessment) performed within 12 weeks prior to first trial treatment or planned within 12 months after screening, e.g.,hip replacement * 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 enrolment in this trial * Any investigational or anti-tumour treatment within 4 weeks or 5 half-life period (whichever is shorter) prior to the initial administration of BI 754091. * Presence of other active invasive cancers other than the one treated in this trial within 5 years prior to screening, with the exception of appropriately treated basal-cell carcinoma of the skin, in situ carcinoma of the uterine cervix, or other local tumours considered cured by local 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 Progression of Disease 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 * Inadequate organ function or bone marrow reserve as demonstrated by the following laboratory values: * Absolute neutrophil count \<1.5 x 10\^9/L (\<1500/mm3) * Platelet count \<100 x 10\^9/L * Haemoglobin \<90 g/L (\<9 g/dL) * Alanine aminotransferase (ALT) \>2.5 times the upper limit of normal (ULN) if no demonstrable liver metastases or \>5 times ULN in the presence of liver metastases * Aspartate aminotransferase (AST) \>2.5 times ULN if no demonstrable liver metastases or \>5 times ULN in the presence of liver metastases * Total bilirubin \>1.5 times ULN, except for patients with Gilbert's syndrome who are excluded if total bilirubin \>3.0 x ULN or direct bilirubin \>1.5 x ULN * Creatinine \>1.5 times ULN or creatinine clearance \<50 mL/min (measured or calculated by Chronic Kidney Disease Epidemiology (CKD-EPI) Collaboration equation); confirmation of creatinine clearance is only required when creatinine is \>1.5 times ULN. * 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 Electrocardiograms, 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 known to prolong the QT interval * Ejection fraction (EF) \<55% 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 \[ECHO\], 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. * History of 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 BI 754091 * Active autoimmune disease or a documented history of autoimmune disease, except vitiligo or resolved childhood asthma/atopy * Known history of human immunodeficiency virus infection or an active hepatitis B or C virus infection. HIV infection is allowed for patients in cohort 6 (cervical/anal squamous) and cohort 7 (vulvar) * Interstitial lung disease * Chronic alcohol or drug abuse or any condition that, in the Investigator's opinion, makes him/her an unreliable trial subject, unlikely to complete the trial, or unable to comply with the protocol procedures.