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.