Study of Furmonertinib in Patients With Advanced or Metastatic Non-Small Cell Lung Cancer (NSCLC) With Activating, Including Uncommon, Epidermal Growth Factor Receptor (EGFR) or Human Epidermal Growth Factor Receptor 2 (HER2) Mutations

Key Inclusion Criteria: * Histologically or cytologically documented, locally advanced or metastatic Non-Small Cell Lung Cancer (NSCLC) not amenable to curative surgery or radiotherapy. * Disease that has progressed after at least one available standard therapy; or for whom standard therapy has proven to be ineffective or intolerable; or for whom a clinical trial of an investigational agent is a recognized standard of care. * Documented radiologic disease progression during or after the last systemic anti-cancer therapy before the first dose of furmonertinib. * For patients with Epidermal Growth Factor Receptor (EGFR) mutations sensitive to osimertinib, the patient must have received osimertinib prior to study enrollment in regions where osimertinib is approved, including the US. Stage 1 dose escalation and backfill cohorts and Stage 2 Cohorts 1, 2, 3 and 4: -Patients with CNS metastases (including leptomeningeal disease) may be eligible if meeting additional protocol specified criteria. Stage 1 Dose Escalation and Backfill Cohorts Inclusion Criteria: \- Documented validated results from local testing of tumor tissue or blood confirming the presence of an activating, including uncommon, EGFR mutation or HER2 exon 20 insertion mutation performed at a CLIA-or equivalently certified laboratory. Stage 2 Cohort 1 Previously Treated, Locally Advanced or Metastatic NSCLC Patients with EGFR Exon 20 Insertion Mutations Inclusion Criteria * Documented validated results from local testing of either tumor tissue or blood confirming the presence of EGFR Exon 20 insertion mutations, performed at a CLIA- or equivalently certified laboratory. * The patient must have experienced disease progression or have intolerance to treatment with platinum-based chemotherapy. Stage 2 Cohort 2 Previously treated, Locally Advanced or Metastatic NSCLC Patients with HER2 Exon 20 Insertion Mutations Inclusion Criteria * Documented validated results from local testing of either tumor tissue or blood confirming the presence of HER2 Exon 20 insertion mutations, performed at a CLIA- or equivalently certified laboratory. * The patient must have experienced disease progression or have intolerance to treatment with platinum-based chemotherapy. * In regions in which fam-trastuzumab deruxtecan-nxki is approved and available for adult patients with unresectable or metastatic NSCLC whose tumors have activating HER2 exon 20 mutations, the patient must have received or be considered not appropriate to receive fam-trastuzumab deruxtecan-nxki. Stage 2 Cohort 3 Previously Treated, Locally Advanced or Metastatic NSCLC Patients with EGFR Activating Mutations Mutations, who are not eligible for Cohorts 1 and 4 Inclusion Criteria * Documented validated results from local testing of either tumor tissue or blood confirming the presence of an EGFR activating mutation, performed at a CLIA- or equivalently certified laboratory. * The patient must have experienced disease progression or have intolerance to treatment with the standard of care EGFR TKI. * Patients with CNS metastases may be eligible if meeting additional protocol specified criteria. Stage 2 Cohort 4 Untreated or Previously Treated EGFR TKI-Naïve, Locally Advanced or Metastatic NSCLC Patients with EGFR Uncommon Mutations excluding EGFR Exon 20 insertions Inclusion Criteria * Previously untreated in the locally advanced or metastatic setting or have progressed after at least 1 available standard therapy, or for whom standard therapy has proven to be ineffective, intolerable, or considered inappropriate * Documented validated results from local testing of either tumor tissue or blood confirming the presence of an EGFR Uncommon mutation, performed at a CLIA- or equivalently certified laboratory a. Representative mutations include, but are not limited to, G719X, S768I, E709X, G779F, L747X, V774M, E709\_T710delinsD, R776C/H, G724S, E736K, I740\_K745dup, N771G, K757M/R, V769L/M, T854X, T751\_I759delinsN Key Exclusion Criteria: * Treatment with chemotherapy, targeted therapy, biologic therapy or an investigational agent as anti-cancer therapy within 3 or 3 elimination weeks or five half-lives prior to initiation of furmonertinib, whichever is shorter, or endocrine therapy within 2 weeks prior to initiation of furmonertinib. * Radiation therapy as cancer therapy within 4 weeks prior to initiation of furmonertinib. * Palliative radiation to bone metastases within 2 weeks prior to initiation of furmonertinib. * AE from prior anticancer therapy that have not resolved to Grade ≤ 1 except for alopecia or Grade ≤ 2 peripheral neuropathy. Stage 2 Cohort 4 Untreated or Previously Treated EGFR TKI-Naïve, Locally Advanced or Metastatic NSCLC Patients with EGFR Uncommon Mutations Exclusion Criteria * Prior treatment with any EGFR TKIs * Progression during neoadjuvant or adjuvant therapy (e.g., chemotherapy, radiotherapy, immunotherapy or investigational agents) or within 12 months of completion of above therapies.