• Patients must have histologically or cytologically documented locally advanced or metastatic KRAS\^G12C-mutant NSCLC that has previously been treated with a KRAS\^G12C inhibitor AND an immune checkpoint inhibitor (ICI) AND chemotherapy, either given concurrently or sequentially, UNLESS they have any contra-indications to any drug class described above

• Patients must have KRAS\^G12C mutation identified by tumor tissue or plasma circulating tumor deoxyribonucleic acid (ctDNA) profiling using a Clinical Laboratory Improvement Act (CLIA) certified College of American Pathologists (CAP) accredited platform; local molecular testing will be allowed. Testing must have been done within the last 5 years before enrollment in this study

• Data must be available for which prior KRAS\^G12C inhibitor treatment the patient has received and the dates that they received it (type of KRAS\^G12C inhibitor used and start and end dates must be collected prior to enrollment)

• Data must be available on the date patients received the last dose of KRAS\^G12C inhibitor and the date of disease progression on their last treatment prior to screening for this trial. Data must be available on the last treatment they received and if it was not or did not include a KRAS\^G12C inhibitor. The time between last KRAS\^G12C inhibitor and treatment on this trial will be collected prior to enrollment

• Data must be available on historical HER2 immunohistochemistry (IHC) status (date of test, type of antibody used for the IHC test, scoring system (i.e., breast versus \[vs.\] gastric), and results must be collected prior to enrollment). Patients must also have ERBB2 (HER2) mutations status identified by tumor tissue or plasma ctDNA profiling; local (i.e., commercial or institutional next generation sequencing \[NGS\]) molecular testing will be allowed. Patients who do not have this information available for collection will not be enrolled on this study

• Patients must have measurable disease, as defined by RECIST v1.1 using computed tomography (CT) or magnetic resonance imaging (MRI). Previously irradiated lesions cannot be counted as target lesions unless there has been demonstrated progression in the lesions since radiotherapy and no other lesions are available for selection as target lesions

• Age ≥ 18 years at date of informed consent form signature

⁃ Because no dosing or adverse event data are currently available on the use of sotorasib (AMG-510) in combination with trastuzumab deruxtecan (DS-8201a) in patients \< 18 years of age, children are excluded from this study

• Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 (Karnofsky ≥ 60%)

• Hemoglobin ≥ 9 g/dL (within 14 days of enrollment)

• Leukocytes ≥ 3,000/mcL (within 14 days of enrollment)

• Absolute neutrophil count ≥ 1,500/mcL (within 14 days of enrollment)

⁃ No administration of granulocyte colony stimulating factor (G-CSF) is allowed within 1 week prior to screening assessment

• Platelets ≥ 100,000/mcL (within 14 days of enrollment)

⁃ No transfusions with red blood cells or platelets are allowed within 1 week prior to screening assessment

• Total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN) (within 14 days of enrollment), (\< 3 x ULN in the presence of documented Gilbert's syndrome or liver metastases at baseline)

• Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT)(serum glutamic pyruvic transaminase \[SGPT\]) ≤ 3 x institutional ULN (within 14 days of enrollment) (\< 5 x ULN in participants with liver metastases)

• Serum albumin ≥ 2.5 g/dL (within 14 days of enrollment)

• International normalized ratio (INR)/prothrombin time (PT) and activated partial thromboplastin time (aPTT) ≤ 1.5 x ULN (within 14 days of enrollment)

• Creatinine ≤ 1.5 x institutional ULN OR creatinine clearance (CrCL) ≥ 30 mL/min/ as determined by (using actual body weight) (within 14 days of enrollment)

• Patients must have left ventricular ejection fraction (LVEF) ≥ 50% by either an echocardiogram (ECHO) or multigated acquisition (MUGA) scan within 28 days before enrollment

• Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial

• For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated

• Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load

• Patients with treated brain metastases are eligible with 1 day washout for stereotactic radiosurgery (SRS) and 2 weeks washout for whole brain radiation (WBRT)

• Patients with new or progressive brain metastases (active brain metastases) are eligible if the treating physician determines that immediate central nervous system (CNS) specific treatment is not required and is unlikely to be required during the first cycle of therapy

• Patients must have a life expectancy of ≥ 12 weeks

• Patients must have a corrected QT interval (QTc) ≤ 470 msec for women and ≤ 450 msec for men (based on average screening triplicates)

• Patients must be willing to undergo a mandatory pre-treatment biopsy (28 days before treatment starts on cycle 1 day 1 \[C1D1\]) for patients enrolled into the expansion phase (phase II). The pre-treatment biopsy is optional for patients enrolled into the dose escalation phase (phase I)

• Patients must have the ability to ingest and retain oral (PO) medications

• The effects of the combination of sotorasib (AMG-510) and trastuzumab deruxtecan (DS-8201a) on the developing human fetus are unknown. For this reason and because HER-2-directed antibody conjugated to a topoisomerase 1 inhibitor agents are known to be teratogenic, women of child-bearing potential (WOCBP) must agree to use dual methods of contraception and must have a negative serum pregnancy testing at screening. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Women treated or enrolled on this protocol must agree to use a highly effective method of contraception, if sexually active, or avoid intercourse during the study treatment and for 7 months following the last dose of study drug. Sotorasib (AMG-510) may reduce the effectiveness of hormonal contraceptives, and therefore women using hormonal contraceptives should add a barrier method on study and for an additional 7 days after the last dose of sotorasib (AMG-510). Men treated or enrolled on this protocol must also agree to use a highly effective barrier method of contraception, if sexually active, or avoid intercourse throughout the duration of the study and for 4 months following the last dose of study drug. To prevent exposure of the unborn child to sotorasib (AMG-510) through semen, male subjects will be required to practice true sexual abstinence (not have sex) or must wear a condom during vaginal sex

• Women of non-child-bearing potential defined as pre-menopausal females with a documented tubal ligation or hysterectomy; or postmenopausal defined as 12 months of spontaneous amenorrhea (in questionable cases, a blood sample with simultaneous follicle-stimulating hormone \[FSH\] \> 40 mIU/mL and estradiol \< 40 pg/mL \[\< 147 pmol/L\] is confirmatory) are eligible. Females on hormone replacement therapy (HRT) and whose menopausal status is in doubt will be required to use one of the contraception methods outlined for women of child-bearing potential if they wish to continue their HRT during the study. Otherwise, they must discontinue HRT to allow confirmation of post-menopausal status prior to study enrollment. For most forms of HRT, at least 2-4 weeks will elapse between the cessation of therapy and the blood draw; this interval depends on the type and dosage of HRT. Following confirmation of their post-menopausal status, they can resume use of HRT during the study without use of a contraceptive method

• Male subjects must not freeze or donate sperm starting at screening and throughout the study period, and at least 4 months after the final study drug administration. Preservation of sperm should be considered prior to enrollment in this study

• Female subjects must not donate, or retrieve for their own use, ova from the time of screening and throughout the study treatment period, and for at least 7 months after the final study drug administration

• Ability to understand and the willingness to sign a written informed consent document. Legally authorized representatives may sign and give informed consent on behalf of study participants