Phase 1/2 Trial of Selinexor (KPT-330) With Docetaxel for Non-small Cell Lung Cancer (NSCLC)

Inclusion Criteria: * Patients must meet all of the following inclusion criteria to be eligible to enroll in this study: 1. Written informed consent in accordance with federal, local, and institutional guidelines. The patient must provide informed consent prior to the first screening procedure. However, the Investigator should not repeat procedures that are performed as part of standard of care (SOC), if they are within the screening window and are done prior to signing the ICF. 2. Age ≥ 18 years 3. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 4. Histologically or cytologically confirmed advanced (stage 4, according to the American Joint Committee on Cancer \[AJCC\] version 7.0 Staging manual) NSCLC 5. Molecular identification of a KRAS mutation (codons 12, 13, or 61 mutations detected by sequencing) by a CLIA-certified assay (source documentation required). 6. Tissue available for analysis at time of enrollment for biomarker analysis: 10 unstained slides plus 1 H+E slide. If archival tumor tissue is not available in select cases, subjects may be permitted to enroll on the study with prior approval of the study PI. 7. At least one and up to two previous lines of systemic cytotoxic therapy for advanced NSCLC, of which one must have been a platinum-based doublet therapy. Up to four total previous lines of systemic therapy (including immunotherapy and molecularly targeted therapy) for advanced NSCLC. 8. Radiographic or clinical disease recurrence or progression during or after the last line of systemic therapy 9. Adequate hematologic function (absolute neutrophil count \[ANC\] ≥ 1500 cells/µL; hemoglobin ≥ 9 g/dL; platelets ≥ 100,000/µL. Patients may be transfused with PRBCs up to 7 days prior to when enrollment labs are drawn to achieve Hgb ≥9.0 mg/dL. 10. Adequate renal function (calculated creatinine clearance ≥ 30 mL/min using the Cockcroft-Gault equation) 11. Adequate hepatic function (total bilirubin ≤ upper limit of normal \[ULN\], alanine aminotransferase \[ALT\] ≤ 2 × ULN and aspartate aminotransferase \[AST\] ≤ 2 × ULN). ALT and/or AST may be ≤ 5 × ULN if due to liver metastases. If ALT or AST is \> 2 and ≤ 5 × ULN in patients with liver metastases, alkaline phosphatase must be ≤ 2.5 × ULN (unless elevated alkaline phosphatase clearly due to skeletal-rather than hepatic-process; eg, normal GGT, presence of multiple bone metastases, absence of bulky and/or central liver metastases). Patients with Gilbert's syndrome are allowed if total bilirubin ≤ 2 × ULN and direct bilirubin is ≤ ULN. 12. Female patients of childbearing potential must agree to use 2 methods of contraception (including 1 highly effective and 1 effective method of contraception) and have a negative serum pregnancy test at Screening. Male patients must use an effective barrier method of contraception if sexually active with a female of childbearing potential. For both male and female patients, effective methods of contraception must be used throughout the study and for 3 months following the last dose of study treatment. Female patients of child-bearing potential must have a negative serum pregnancy test at screening and agree to use 2 reliable methods of contraception throughout the study and for 3 months after their last dose of medication. Female patients are considered NOT of childbearing potential if they have a history of surgical sterility (including hysterectomy and/or bilateral oophorectomy, but not tubal ligation alone) or evidence of post-menopausal status defined as any of the following: * Natural menopause with last menses \>1 year ago * Radiation-induced oophorectomy with last menses \>1 year ago * Chemotherapy-induced menopause with last menses \>1 year ago. Male patients and their partners must use 2 reliable methods of contraception, at least one of them a barrier method (if sexually active with a female of child-bearing potential). 13. Measurable disease according to RECIST v1.1 14. Previously treated (surgery and/or radiation therapy) or untreated brain metastases are eligible, provided that patients are asymptomatic and not requiring escalating doses of corticosteroids. 15. Previous treatment-associated clinically significant toxicities resolved to CTCAE grade ≤2 (except alopecia) or to their baseline. NOTE: Prior immunotherapy-related endocrinopathy controlled with ongoing medical management (eg, hypothyroidism, adrenal insufficiency, diabetes) is permitted 16. At least 3 weeks or 5 half-lives, whichever is shorter, since receiving systemic anticancer therapy, including investigational agents, prior to starting study therapy. At least 2 weeks since receiving radiation therapy prior to starting study therapy Exclusion Criteria: * Patients meeting any of the following exclusion criteria are not eligible to enroll in this study: 1. Patients who are pregnant or lactating 2. Major surgery (excluding skin biopsies and procedures for insertion of central venous access devices) within 2 weeks of first dose of study drug 3. Any life-threatening illness, medical condition or organ system dysfunction which, in the investigator's opinion, could compromise the patient's safety 4. Concurrent active malignancy that would interfere with treatment administration or assessment in the opinion of the treating investigator 5. Unstable cardiovascular function: * Symptomatic ischemia, or * Uncontrolled clinically significant conduction abnormalities (i.e., ventricular tachycardia on anti-arrhythmics is excluded; 1st degree AV block or asymptomatic LAFB/RBBB are not excluded; asymptomatic rate controlled atrial fibrillation is not excluded), or * Congestive heart failure (CHF) of NYHA Class ≥3, or * Myocardial infarction (MI) within 3 months 6. Uncontrolled (i.e., clinically unstable) infection requiring parenteral antibiotics, antivirals, or antifungals within one week prior to first dose; however, prophylactic use of these agents is acceptable even if parenteral 7. Pre-existing grade 3 or 4 neuropathy 8. Active Hepatitis A, B or C infection 9. Known human immunodeficiency virus (HIV) infection (HIV testing is not required as part of this study) 10. Patients unable to swallow tablets, patients with malabsorption syndrome, or any other GI disease or GI dysfunction that could interfere with absorption of study treatment 11. Prior exposure to docetaxel, selinexor, or another selective inhibitor of nuclear transport (SINE) compound (NOTE: prior docetaxel exposure permitted in selinexor monotherapy cohort) 12. Patients unwilling to comply with study protocol.