Testing the Safety and Tolerability of the Anti-cancer Drugs Trastuzumab Deruxtecan and Neratinib for Cancers With Changes in the HER2 Gene

Inclusion Criteria: * Patients must have histologically confirmed malignancy that is metastatic or unresectable with participation in this clinical trial determined to be the best option for next treatment in the opinion of the investigator, and meet the following specific criteria: * Patients enrolling in Part 1 (Dose Escalation) may have a diagnosis of any solid tumor * Patients enrolling in the Part 2 Pharmacodynamic Cohort may have a diagnosis of any solid tumor except pancreas cancer (NOTE: pancreatic cancer excluded from this cohort after Revision 11 activation due to the addition of the pancreatic specific cohort) * Patients enrolling in the Part 2 Pancreatic Cohort must have a diagnosis of pancreatic adenocarcinoma (PDAC) and meet the HER2 positivity guidance * Patients must have a solid tumor with HER2-positivity as determined by any one or more of the following: * HER2 overexpression defined by immunohistochemistry (IHC) 3+ * ERBB2 amplification by in situ hybridization (ISH) or next-generation sequencing as determined by any Clinical Laboratory Improvement Act (CLIA) certified lab * A known HER2 activating mutation * HER2 overexpression by IHC/ISH will follow histology specific American Society of Clinical Oncology (ASCO)-College of American Pathologists (CAP) guidelines for breast and gastric cancers. HER2 overexpression by IHC/ISH for the Pancreatic Cohort will follow ASCO-CAP guidelines for gastric cancers. For tumor histologies without specific guidelines the following criteria will apply: * HER2 IHC should be performed first, followed by ISH methods in cases showing 2+ (equivocal) expression by IHC. Positive (IHC 3+) or negative (IHC 0 or 1+) do not require further ISH testing. Cases with HER2:CEP17 ratio ≥ 2 or an average HER2 copy number ≥ 6.0 signals per cell are considered positive by ISH * Known HER2 activating mutations: * G309A/E * S310F/Y * S653C * V659E * G660D * R678Q * E693K * Q709L * L755S/P * Del. 755-759 * D769Y/H * G776V/C * V777L * V842I * T862A * L869R * H878Y * All exon 20 insertions, including: * A771\_Y772insYVMA * A775\_G776insYVMA * Y772\_A775dup * P780\_Y781insGSP * G778\_P780dup * V697L * T733I * D769N * L841V * L866M * R896C * If a different mutation is identified, contact the study chair for conferral. Synonymous mutations are not eligible * Patients must have received at least 1 prior line of therapy in the advanced/metastatic setting. No limitation on number of prior therapies; however, patients may not have received neratinib or DS-8201a previously. Prior HER2-targeted therapy other than neratinib or DS-8201a is allowed (e.g., trastuzumab, pertuzumab, TDM-1, lapatinib, etc.) * Age \>= 18 years. Because no dosing or adverse event data are currently available on the use of neratinib in combination with DS-8201a in patients \< 18 years of age, children are excluded from this study * Patients must have Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 70%) * Hemoglobin \>= 9.0 g/dL (\>= 8.0 g/dL for gastric cancer \[GC\] only) (within 14 days of enrollment) * No transfusions with red blood cells or platelets are allowed within 1 week prior to screening assessment * Leukocytes \>= 3.0 K/cumm (within 14 days of enrollment) * Absolute neutrophil count \>= 1.5 K/cumm (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 K/cumm (within 14 days of enrollment) * No transfusions with red blood cells or platelets are allowed within 1 week prior to screening assessment * Serum albumin \>= 2.5 g/dL (within 14 days of enrollment) * Total bilirubin =\< 1.5 × institutional upper limit of normal (ULN), (\< 3 × ULN in the presence of documented Gilbert's syndrome or liver metastases at baseline) (within 14 days of enrollment) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x ULN (if liver metastases are present =\< 5 x ULN) (within 14 days of enrollment) * International normalized ratio (INR)/prothrombin time (PT) and activated partial thromboplastin time (aPTT) =\< 1.5 x institutional ULN (within 14 days of enrollment) * This applies only to patients who are not receiving therapeutic anticoagulation that may affect INR. Those who are on therapeutic anticoagulation, should be on a stable dose for 4 weeks and should be considered within therapeutic range * Creatinine =\< 1.5 x institutional ULN OR Glomerular filtration rate (GFR) \>= 30 mL/min/1.73 m\^2 (using the Cockcroft-Gault equation) (within 14 days of enrollment) * Patients who are human immunodeficiency virus (HIV)-positive may participate IF they meet the following eligibility requirements: * They must be stable on their anti-retroviral regimen, and they must be healthy from an HIV perspective * They must have a CD4 count of greater than 250 cells/mcL over the past 6 months on this same anti-retroviral regimen and must not have had a CD4 count \< 200 cells/ul over the past 2 years, unless it was deemed related to THE CANCER AND/OR CHEMOTHERAPY-induced bone marrow suppression * For patients who have received chemotherapy in the past 6 months, a CD4 count \< 250 cells/ul during chemotherapy is permitted as long as viral loads were undetectable during this same chemotherapy * They must have an undetectable viral load and a CD4 count \>= 250 cells/uL within 7 days of enrollment * They must not be currently receiving prophylactic therapy for an opportunistic infection and must not have had an opportunistic infection within the past 6 months. HIV-infected patients should be monitored every 12 weeks for viral load and CD4 counts * For patients with evidence of c