Trastuzumab Deruxtecan (DS-8201a) for the Treatment of Recurrent or Refractory Osteosarcoma, Wilms Tumor, and Desmoplastic Small Round Cell Tumor

Inclusion Criteria: * Phase 1 (Part A): Patients must be at least 2 years and less than 12 years of age at the time of study enrollment * Phase 2: Wilms tumor patients (Part B1): All Wilms tumor patients enrolled must be less than 18 years of age at enrollment * Until the completion of the Phase 1 dose confirmation, patients must be at least 12 years of age and less than 18 years of age at the time of study enrollment * Following dose confirmation of DS-8201a in children at least 2 to less than 12 years old in the Phase 1 component, Wilms tumor patients at least 2 to less than 18 years of age will be allowed on the Phase 2 component * Phase 2: DSRCT patients (Part B2): Until the completion of the Phase 1 component, patients enrolling on the Phase 2 component of the study must be from at least 12 to 39 years of age at the time of study enrollment * Following dose confirmation of DS-8201a in children at least 2 to less than 12 years old in the Phase 1 component, DSRCT patients at least 2 to 39 years of age will be allowed on the Phase 2 component * Patients must have had histologic verification of Wilms tumor or desmoplastic small round cell tumor at original diagnosis or relapse * Solid tumors: Patients must have measurable disease according to Response Evaluation Criteria in Solid Tumors (RECIST) 1.1. Patients with clinically inactive brain metastases may be included in the study. Patients with treated brain metastases that are no longer symptomatic and who require no treatment with corticosteroids or anticonvulsants may be included in the study if they have recovered from the acute toxic effect of radiotherapy. Lastly, patient must have unresectable lesions or lesions with no intention to surgically remove the lesions in the 6 months following enrollment * Wilms tumor: WT patients must have either refractory disease or a very high risk relapse, defined as ANY of the following: * Relapse after initial treatment with 4 or more chemotherapy agents (e.g. Regimens vincristine, dactinomycin, doxorubicin, cyclophosphamide, etoposide and radiation \[M\], vincristine, dactinomycin and doxorubicin, vincristine, and irinotecan \[MVI\], doxorubicin, vincristine, cyclophosphamide, carboplatin, etoposide and radiation \[UH-1\], doxorubicin, vincristine, cyclophosphamide, carboplatin, etoposide, vincristine, and irinotecan \[UH-2\], vincristine, irinotecan, cyclophosphamide, carboplatin, etoposide and doxorubicin \[UH-3\], and etoposide, carboplatin, cyclophosphamide, and doxorubicin \[HR-1\]) * Relapse with high risk histology (anaplasia, blastemal predominant) * Multiple relapses * Desmoplastic small round cell tumor: DSRCT patients with relapsed or refractory disease are eligible * Patient's current disease state must be one for which they have received at least standard initial therapy, defined as systemic therapy combined with either radiation or surgery for local control of the primary tumor at diagnosis. Prior therapy after relapse is not required * Patients must have a performance status corresponding to Eastern Cooperative Oncology Group (ECOG) scores of 0 or 1. Use Karnofsky for patients older than 16 years of age and Lansky for patients 16 years of age and younger * Patients must have recovered from the acute toxic effects of all prior anti-cancer therapy and must meet the following minimum duration from prior anti-cancer directed therapy prior to enrollment. If after the required timeframe, the numerical eligibility criteria are met, e.g., blood count criteria, the patient is considered to have recovered adequately * Cytotoxic chemotherapy or other anti-cancer agents known to be myelosuppressive: For agents not listed, the duration of this interval must be discussed with the study chair and the study-assigned Research Coordinator prior to enrollment * \>= 21 days after the last dose of myelosuppressive chemotherapy (42 days if prior nitrosourea) * Anti-cancer agents not known to be myelosuppressive (e.g., not associated with reduced platelet or absolute neutrophil count \[ANC\] counts): \>= 7 days after the last dose of agent * Antibodies: \>= 4 weeks (28 days) must have elapsed from infusion of last dose of antibody, and toxicity related to prior antibody therapy must be recovered to grade =\< 1 * Corticosteroids * Hematopoietic growth factors: \>= 14 days after the last dose of a long-acting growth factor (e.g. pegfilgrastim) or 7 days for short-acting growth factor. For agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur * Interleukins, interferons and cytokines (other than hematopoietic growth factors): \>= 21 days after the completion of interleukins, interferon or cytokines (other than hematopoietic growth factors) * Stem cell Infusions (with or without total body irradiation \[TBI\]): * Allogeneic (non-autologous) bone marrow or stem cell transplant, or any stem cell infusion including donor lymphocyte infusion (DLI) or boost infusion: \>= 84 days after infusion and no evidence of graft versus host disease (GVHD) * Autologous stem cell infusion including boost infusion: \>= 30 days * Cellular therapy: \>= 30 days after the completion the infusion of any type of cellular therapy (e.g., modified T cells, natural killer \[NK\] cells, dendritic cells, etc.) * Radiation therapy (XRT)/external beam irradiation including protons: \>= 4 weeks (28 days) including palliative radiation therapy to the chest. \>= 14 days after palliative local XRT to areas other than the chest or for whole brain radiotherapy * Radiopharmaceutical therapy (e.g., radiolabeled antibody, samarium): \>= 42 days after systemically administered radiopharmaceutical therapy * Patients must not have received prior HER2 therapies including antibody drug conjugates (e.g. TDM-1 or DS-8201a), HER2 directed cellular therapies, HER2 receptor therapy (e.g