Testing Afatinib as Potentially Targeted Treatment in Cancers With EGFR Genetic Changes (MATCH - Subprotocol A)

Inclusion Criteria:

* Patients must have met applicable eligibility criteria in the Master MATCH Protocol EAY131/ NCI-2015-00054 prior to registration to treatment subprotocol
* Patients must fulfill all eligibility criteria of MATCH Master Protocol at the time of registration to treatment step (Step 1, 3, 5, 7)
* Patient's tumor must have either of the below, or another aberration, as determined via the MATCH Master Protocol:

  * Activating mutations of EGFR (del 19, L858R) OR
  * Any malignancy harboring any of the following mutations: EGFR G719A, G719C, G719D, G719S EGFR L861Q, EGFR S768I
  * Tumors with an exon 20 insertion alone without the above mutations will be excluded, with the exception of exon 20 insertions approved as inclusion variants as part of the dynamic actionable mutation of interest (aMOI) process
* Patients must have an electrocardiogram (ECG) within 8 weeks prior to treatment assignment and must have no clinically important abnormalities in rhythm, conduction or morphology of resting ECG (e.g. complete left bundle branch block, third degree heart block)
* Patients with known left ventricular dysfunction must have ECHO or a nuclear study (multigated acquisition scan \[MUGA\] or first pass) within 4 weeks prior to registration to treatment and must not have left ventricular ejection fraction (LVEF) \< institutional lower limit of normal (LLN). If the LLN is not defined at a site, the LVEF must be \> 50% for the patient to be eligible

  * NOTE: Pre-treatment LVEF determination in patients without known left ventricular dysfunction is NOT otherwise required
* Patients must not have known hypersensitivity to afatinib or compounds of similar chemical or biologic composition
* Patients must have =\< grade 1 renal function as defined below:

  * Creatinine =\< 1.5 x normal institutional limits OR
  * Measured creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal or as calculated by the Cockcroft-Gault equation
  * The above renal eligibility criteria should be strictly followed and will override the MATCH Master Protocol requirements
* Patients must not have had prior treatment with an EGFR tyrosine kinase inhibitor (TKI) (e.g. afatinib, erlotinib, gefitinib, neratinib, dacomitinib, AZD9291, cabertinib, CO-1686)
* Patients with non-small cell lung cancer and small cell lung cancer will be excluded
* Patients with a history of interstitial lung disease will be excluded
* Patients with glioblastoma multiforme (GBM) will be excluded
* Patients must have =\< grade 1 diarrhea at baseline