A Study of NX-019 in Patients with Advanced, Epidermal Growth Factor Receptor (EGFR) Mutant Cancer

Inclusion Criteria: * Histologically confirmed, locally advanced, or metastatic EGFR-mutant cancer and has progressed on or are intolerant to all standard therapy. * Patients with non-small cell lung cancer (NSCLC) harboring a mutation that is sensitive to osimertinib must have received osimertinib prior to enrollment. * Measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 (evaluable disease acceptable for dose escalation part of study). * ≥18 years of age (or age of consent in in accordance with local law). * Life expectancy ≥3 months. * Adequate organ and bone marrow function. * All patients will have a baseline magnetic resonance imaging (MRI) of the brain. * Resolution of any clinically significant toxic effects of prior therapy to Grade 0 or 1 according to the National Cancer Institute CTCAE v5.0 (exception of alopecia and Grade 2 peripheral neuropathy). * Eastern Cooperative Oncology Group (ECOG) performance status of ≤2. * Willingness of men and women of reproductive potential to observe conventional and effective birth control methods with failure rates of \<1% for the duration of treatment and for 6 months following the last dose of study treatment. * A negative serum pregnancy test at Screening and a negative (serum or urine) pregnancy test within 72 hours before the first dose of study drug (female patients of childbearing potential only). * Willing and able to give informed consent and comply with protocol requirements for the duration of the study. Specific Inclusion Criteria for Expansion Cohorts: To be eligible during the expansion part of the study, patients must meet the above inclusion criteria, and the criteria for 1 of the following cohorts: Expansion Cohort 1: * Patients with NSCLC with EGFR exon 19 deletions or exon 21 L858R mutations who have progressed on or after prior EGFR TKI therapy. Expansion Cohort 2: * Patients with NSCLC with EGFR ex20ins mutations, who are not suitable for, or are unwilling to receive available ex20ins mutation targeted therapy. Expansion Cohort 3: * Patients with NSCLC with EGFR mutations for which there is no current targeted therapy, (i.e., exclusion of exon 19, exon 21 L858R, and ex20ins mutation). Exclusion Criteria: Patients who meet any of the following criteria will be excluded from participation in the study: * Known C797X EGFR mutations or 1 or more known secondary drivers of disease. * Disease requiring immediate palliative treatment with surgery or radiation therapy. * Requirement for greater than 4 mg/day of dexamethasone (or equivalent) for management of CNS metastases. * Received systemic anticancer chemotherapy, targeted agents, antibody therapy for cancer, immunotherapy for cancer, hormonal therapy or an investigational agent within 2 weeks or 5 half-lives (whichever is shorter) prior to start of study drug treatment. * Major surgery within 3 weeks prior to start of study drug treatment. * Radiation therapy within 4 weeks prior to start of study drug treatment. * Severe or unstable cardiac conditions within 6 months prior to starting study drug treatment. * Severe or unstable medical condition including uncontrolled diabetes or unstable psychiatric condition. * Dependent on contact lenses (unable to wear eyeglasses) and unable to comply with ophthalmic guidance. * History of interstitial lung disease, radiation pneumonitis which required systemic steroid therapy, or other significant lung disease. * Another active malignancy within the previous 2 years except for localized cancers that are not related to the current cancer being treated, are considered cured, and, in the opinion of the Investigator, present a low risk of recurrence. * Active infection requiring systemic therapy. * Known human immunodeficiency virus (HIV), hepatitis B virus (HBV) (i.e., hepatitis B surface antigen-positive), or hepatitis C virus (HCV) (i.e., detectable HCV ribonucleic acid \[RNA\]). * Active gastrointestinal disease (e.g., Crohn's disease, ulcerative colitis, or short gut syndrome) or conditions that may impact drug absorption. * Pregnant or breastfeeding. * Is using a strong CYP3A inhibitor or inducer, and cannot refrain from use from 7 days prior to the first dose and throughout the study. * Is using a proton pump inhibitor and cannot refrain from use from 7 days prior to the first dose and throughout the study. * Is using a sensitive substrate of P-gp with a narrow therapeutic window (e.g. digoxin). * Any other condition, including significant skin or nail disease, that in the opinion of the Investigator would place the patient at an unacceptable risk or cause the patient to be unlikely to fully participate or comply with study procedures.