Inclusion Criteria:  Histologically or cytologically confirmed advanced or metastatic NSCLC (small cell or mixed histologies are excluded). Documented disease progression after treatment with at least one prior systemic therapy for advanced disease. Participants who do not have standard of care access due to any reason, are intolerant to, are not eligible for, or refuse standard treatments, may also be eligible. Adequate archival tumor tissue (ideally taken after last targeted treatment and not older than 6 months) has to be available, either from primary or metastatic sites. If archival material is not available, fresh biopsy derived from a non-significant risk procedure can be considered at the Investigator´s discretion. Measurable disease by RECIST v1.1 with at least one lesion that can be accurately measured at baseline with computed tomography (CT) or magnetic resonance imaging (MRI) which is suitable for accurate repeated measurements. Previously irradiated lesions must have shown progression to be considered measurable. Lesions that would be biopsied during the study are not considered measurable. Documented activating EGFR and/or HER2 mutation assessed by a Clinical Laboratory Improvement Amendments (CLIA)-certified (United States [US] sites) or an equally accredited (outside of the US) local laboratory Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1. Minimum life expectancy of 12 weeks.  Adequate bone marrow function as assessed by the following laboratory tests to be conducted within 7 days before the first dose of study treatment:  Hemoglobin ≥ 9.0 g/dL. Criteria must be met without erythropoietin dependency and without packed red blood cell (pRBC) transfusion within 2 weeks prior to testing. Platelets ≥ 100 × 10*9 cells/L. Absolute neutrophil count ≥ 1.5 ×10*9 cells/L. Criteria must be met without the use of hematopoietic growth factors (e.g., G-CSF) within 2 weeks prior to testing.  Adequate kidney function as assessed by following laboratory test to be conducted within 7 days before the first dose of study treatment:  a. Estimated glomerular filtration rate (eGFR) > 40 mL/min per 1.73 m*2 according to the Modification of Diet in renal Disease Study Group (MDRD) formula.  Adequate liver function as assessed by following laboratory tests to be conducted within 7 days before the first dose of study treatment:  Total bilirubin ≤ 1.5 × ULN (or ≤ 3 X ULN for participants with documented Gilbert-Meulengracht Syndrome, or for participants with hyperbilirubinemia considered due to liver metastasis). Aspartate transaminase and alanine transaminase ≤ 2.5 × ULN (or ≤ 5 × ULN if due to liver involvement by tumor).  Exclusion Criteria:  Treatment with an EGFR tyrosine kinase inhibitor (TKI) ≤ 8 days or 5x the terminal phase, elimination half-lives, whichever is shorter, prior to the first dose of study drug. Treatment with a systemic anti-cancer treatment (excluding EGFR TKIs as described above) ≤ 14 days prior to the first dose of study drug. Radiation therapy and palliative radiation ≤ 14 days prior to the first dose of study drug. If irradiated, lesions must have demonstrated progression prior to be considered for evaluation as target lesions. Treatment with immunotherapy ≤ 28 days prior to the first dose of study drug. Have any unresolved toxicity of Grade ≥ 2 from previous anti-cancer treatment, except for alopecia and skin pigmentation. Participants with chronic, but stable Grade 2 toxicities may be allowed to enroll after agreement between the Investigator and Sponsor. Any history of primary brain or meningeal tumors, presence of symptomatic central nervous system (CNS) metastases, or CNS metastases that require local treatment (such as radiotherapy or surgery).  History of spinal cord compression or brain metastases with the following exception:  a. Participants with treated brain metastases are eligible in Dose Escalation, Backfill and Expansion if there is no evidence of progression (new or enlarging brain metastases) for at least 4 weeks after CNS-directed treatment, as ascertained by clinical examination and brain imaging (MRI or CT) during the screening period. In addition, participants must be requiring stable or decreasing dose of corticosteroids for 7 days prior to first dose of BAY2927088.  History of congestive heart failure (CHF) Class >II according to the New York Heart Association (NYHA) Functional Classification or serious cardiac arrhythmias requiring treatment or any clinically important abnormalities in rhythm, conduction or morphology or resting ECG (e.g., complete left bundle branch block, third degree heart block, second degree heart block, PR interval >250 msec).  Participants with:  Known human immunodeficiency virus (HIV), except as noted below:  Participants with history of HIV infection are eligible at the Investigator's discretion provided that:  CD4+ T-cell (CD4+) counts are ≥ 350 cells/uL The participant has been on established antiretroviral therapy (ART) for at least 4 weeks prior to the start of study drug and has an HIV viral load less than 400 copies/mL prior to start of the study treatment The ART being used does not contain strong inducers or inhibitors of CYP3A4, and is not anticipated to cause overlapping toxicities with study drug The participant has not had an opportunistic infection within the past 12 months Active Hepatitis B infection (positive for Hepatitis B surface antigen [HbsAg]) and Hepatitis B virus [HBV] DNA).  Active Hepatitis C infection (positive anti-HCV Antibody and quantitative HCV RNA results greater than the lower limits of detection of the assay).  NOTE: Participants with history of chronic HBV or HCV infection are eligible at the Investigator's discretion provided that the disease is stable and sufficiently controlled under treatment.  Use of strong CYP3A4 inhibitors and inducers from 14 days prior to first administration of study drug. Strong CYP3A4 inhibitors and inducers (see Section 10.5) are prohibited during the study and until Safety FU (follow up) visit.