Testing the Biological Effects of DS-8201a on Patients With Advanced Cancer

Inclusion Criteria: * Patients must have histologically confirmed malignancy that is metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective * Patients must have measurable or evaluable disease * Age \>= 18 years of age * Patients must have HER2-positive or HER2-expressing tumors as defined by Clinical Laboratory Improvement Act (CLIA)-certified labs. Patients must have either: * A tumor HER2 immunohistochemistry (IHC) score of 1+ or greater (as determined by a CLIA-certified IHC test, per criteria specified) or * A tumor with HER2 amplification (as determined by CLIA-certified in situ hybridization \[ISH\] or a CLIA-certified next-generation sequencing assay) * Patients with HER2 mutations are eligible, as are patients with HER2-positive breast cancer * Patients must have Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 70%) * Absolute neutrophil count \>= 1,500/mcL (within 8 days of enrollment) * Platelets \>= 100,000/mcL (within 8 days of enrollment) * Leukocytes \>= 3,000/mcL (within 8 days of enrollment) * Hemoglobin \>= 9 g/dL (\>= 8.0 g/dL for gastric cancer \[GC\] only) (within 8 days of enrollment) * Serum albumin \>= 2.5 g/dL (GC only) (within 8 days of enrollment) * Total bilirubin =\< 1.5 x institutional upper limit of normal (=\< 3 x upper limit of normal in the presence of documented Gilbert's syndrome or liver metastases at baseline) (within 8 days of enrollment) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x institutional upper limit of normal OR =\< 5 x institutional upper limit of normal for patients with liver metastases at baseline (within 8 days of enrollment) * Creatinine =\< 1.5 x institutional upper limit of normal OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above 1.5 x institutional normal (within 8 days of enrollment) * No transfusions with red blood cells or platelets are allowed within 1 week prior to screening assessment * No administration of granulocyte colony-stimulating factor (G-CSF) is allowed within 1 week prior to screening assessment * International normalized ratio (INR)/prothrombin time (PT) and either partial thromboplastin or activated partial thromboplastin time (aPTT) =\< 1.5 x upper limit of normal (ULN) * Ability to understand and the willingness to sign a written informed consent document * Willingness to provide blood samples for research purposes * Patients must have a lesion or lesions amenable to biopsy and must be willing to undergo 3 core needle biopsy procedures for research purposes * Patients must have left ventricular ejection fraction (LVEF) \>= 50% by either an echocardiogram (ECHO), multigated acquisition (MUGA), or cardiac MRI scan within 28 days prior to enrollment * Patients receiving standard of care androgen deprivation treatment (surgical castration versus luteinizing hormone-releasing hormone \[LHRH\] agonist or antagonist treatment) are eligible to participate in the trial. Patients receiving LHRH agonist or antagonist may continue treatment throughout the duration of this study * 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 immunotherapy-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 8 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 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 if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression for \>= 1 month after treatment of the brain metastases * Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial * The effects of DS-8201a on the developing human fetus are unknown. For this reason and because HER2 antibodies conjugated to topoisomerase 1 inhibitor agents are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control or abstinence) prior to study entry and for the duration of study participation and for at least 7 months after the last dose of study drug. 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. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of DS-8201a administration * 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 * Subjects must not freeze, donate, or retrieve for their own use ova or sperm starting at screening, throughout the study period, and for at least 4.5 months after the final study drug administration. Preservation of sperm or ova should be considered prior to enrollment in this study * Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with DS-8201a, breastfeeding should be discontinued if the mother is treated with DS-8201a Exclusion Criteria: * Patients who have had: * Chemotherapy (including antibody drug therapy, retinoid therapy, hormonal therapy for cancer-with the exception of standard of care androgen deprivation treatment) within: * 4 weeks or five half-lives, whichever is shorter, for small-molecule targeted agents such as 5-fluorouracil-based agents, folinate agents, weekly paclitaxel or * 6 weeks for nitrosoureas or mitomycin C or * Immunotherapy, including monoclonal antibody therapy, within 4 weeks * Patients with any of the following pulmonary-related illnesses: * A history of (non-infectious) interstitial lung disease (ILD)/pneumonitis that required steroids, current ILD/pneumonitis, or for whom suspected ILD/pneumonitis cannot be ruled out by imaging at screening * Clinically severe pulmonary compromise resulting from intercurrent pulmonary illnesses including, but not limited to, any underlying pulmonary disorder (i.e., pulmonary emboli within three months of the study enrollment, severe asthma, severe chronic obstructive pulmonary disease \[COPD\] grade 3-4 per Global Initiative for Obstructive Lung Disease \[GOLD\] criteria, restrictive lung disease, pleural effusion, etc.), and any autoimmune, connective tissue, or inflammatory disorders with potential pulmonary involvement (i.e., Rheumatoid arthritis, Sjogren's, sarcoidosis, etc.), or prior pneumonectomy * Patients who have had radiation therapy within 4 weeks (or palliative stereotactic radiation therapy within 2 weeks) * Patients who have had a major surgery within 4 weeks * Patients who are receiving any other investigational agents * Patients with a medical history of myocardial infarction within 6 months before enrollment, symptomatic congestive heart failure (CHF) (New York Heart Association class II to IV), or with troponin levels consistent with myocardial infarction (as defined according to the assay manufacturer) 28 days prior to enrollment * History of allergic reactions attributed to compounds of similar chemical or biologic composition to DS-8201a (e.g., other topoisomerase I inhibitors) or the inactive ingredients in the drug product * Patients who have a history of severe hypersensitivity reactions to other monoclonal antibodies * Patients with a Fridericia's formula-corrected QT interval (QTcF) prolongation to \> 470 ms (females) or \> 450 ms (males) based on average of the screening triplicate 12-lead electrocardiogram (ECG) * Patients with spinal cord compression or clinically active central nervous system metastases, defined as untreated and symptomatic, or requiring therapy with corticosteroids or anticonvulsants to control associated symptoms * Patients with an uncontrolled infection requiring IV antibiotics, antivirals, or antifungals * Patients with unresolved toxicities from previous anticancer therapy, defined as toxicities (other than alopecia) not yet resolved to grade =\< 1 or baseline. Subjects with chronic grade 2 toxicities (e.g., grade 2 chemotherapy-induced neuropathy) may be eligible per the discretion of the investigator after consultation with the sponsor medical monitor or designee. Subjects should no longer be symptomatic nor require treatment with corticosteroids or anticonvulsants and must have recovered from the acute toxic effect of radiotherapy * Patients with substance abuse or any other medical conditions that would increase the safety risk to the subject or interfere with participation of the subject or evaluation of the clinical study in the opinion of the investigator * Patients with uncontrolled intercurrent illness * Patients with psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because DS-8201a is a HER2 antibody conjugated to a topoisomerase 1 inhibitor agent with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with DS-8201a, breastfeeding should be discontinued if the mother is treated with DS-8201a * Patients are not allowed to receive chloroquine/hydroxychloroquine. Patients receiving chloroquine/hydroxychloroquine require a washout of \> 14 days