Lorvotuzumab Mertansine in Treating Younger Patients With Relapsed or Refractory Wilms Tumor, Rhabdomyosarcoma, Neuroblastoma, Pleuropulmonary Blastoma, Malignant Peripheral Nerve Sheath Tumor, or Synovial Sarcoma

Inclusion Criteria: * Patients must have had histologic verification of one of the malignancies listed below at original diagnosis or at relapse * Primary strata * Wilms tumor * Rhabdomyosarcoma * Neuroblastoma * Secondary strata: miscellaneous CD56-expressing tumors: * Pleuropulmonary blastoma * Malignant peripheral nerve sheath tumor (MPNST) * Synovial sarcoma * Patients must have radiographically measurable disease (with the exception of those with neuroblastoma) * Measurable disease is defined as the presence of at least one lesion on magnetic resonance imaging (MRI) or computed tomography (CT) scan that can be accurately measured with the longest diameter a minimum of 10 mm in at least one dimension (CT scan slice thickness no greater than 5 mm) * Note: the following do not qualify as measurable disease: * Malignant fluid collections (e.g., ascites, pleural effusions) * Bone marrow infiltration except that detected by metaiodobenzylguanidine (MIBG) scan for neuroblastoma * Lesions only detected by nuclear medicine studies (e.g., bone, gallium or positron emission tomography \[PET\] scans) except as noted in patients with neuroblastoma who do not have measurable disease but have MIBG-avid evaluable disease * Elevated tumor markers in plasma or cerebrospinal fluid (CSF) * Previously radiated lesions that have not demonstrated clear progression post radiation * Leptomeningeal lesions that do not meet the measurements noted above * Patients with neuroblastoma who do not have measurable disease but have MIBG-avid evaluable disease are eligible * Patients must have a Lansky or Karnofsky performance status score of \>= 50, corresponding to Eastern Cooperative Oncology Group (ECOG) categories 0, 1 or 2; use Karnofsky for patients \> 16 years of age and Lansky for patients =\< 16 years of age; patients who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score * Patients must have fully recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy prior to entering this study * Patients must have received standard treatment appropriate for their tumor type * Myelosuppressive chemotherapy: patients with solid tumors must not have received myelosuppressive chemotherapy within 3 weeks of enrollment onto this study (6 weeks if prior nitrosourea) * Hematopoietic growth factors: at least 14 days must have elapsed after receiving pegfilgrastim and least 7 days must have elapsed since the completion of therapy with a non-pegylated growth factor * Biologic (anti-neoplastic agent): at least 7 days must have elapsed since completion of therapy with a biologic agent; for agents that have known adverse events occurring beyond 7 days after administration, this period prior to enrollment must be extended beyond the time during which adverse events are known to occur * Monoclonal antibodies: at least 3 half-lives must have elapsed since prior therapy that included a monoclonal antibody * Radiotherapy: \>= 2 weeks must have elapsed since local palliative external beam radiation therapy (XRT) (small port); \>= 6 weeks must have elapsed since treatment with therapeutic doses of MIBG; \>= 3 months must have elapsed if prior craniospinal XRT was received, if \>= 50% of the pelvis was irradiated, or if total body irradiation (TBI) was received; \>= 6 weeks must have elapsed if other substantial bone marrow irradiation was given * Stem cell transplant or rescue without TBI: no evidence of active graft vs. host disease and \>= 2 months must have elapsed since transplant * For patients with solid tumors without bone marrow involvement: peripheral absolute neutrophil count (ANC) \>= 1000/uL * For patients with solid tumors without bone marrow involvement: platelet count \>= 100,000/uL (transfusion independent, defined as not receiving platelet transfusions within a 7 day period prior to enrollment) * For patients with solid tumors and known bone marrow metastatic disease: peripheral absolute neutrophil count (ANC) \>= 750/uL * For patients with solid tumors and known bone marrow metastatic disease: platelet count \>= 75,000/uL (transfusion independent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment) * Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70 mL/min/1.73 m\^2 or a serum creatinine based on age/gender as follows: * Age 1 to \< 2 years: maximum serum creatinine: 0.6 mg/dL in males and females * Age 2 to \< 6 years: maximum serum creatinine: 0.8 mg/dL in males and females * Age 6 to \< 10 years: maximum serum creatinine: 1 mg/dL in males and females * Age 10 to \< 13 years: maximum serum creatinine: 1.2 mg/dL in males and females * Age 13 to \< 16 years: maximum serum creatinine: 1.5 mg/dL in males and 1.4 mg/dL in females * Age \>= 16 years: maximum serum creatinine: 1.7 mg/dL in males and 1.4 mg/dL in females * Total bilirubin =\< 1.5 x upper limit of normal (ULN) for age * Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 110 U/L (for the purpose of this study, the ULN for SGPT is 45 U/L) * Serum albumin \>= 2 g/dL * Shortening fraction of \>= 27% by echocardiogram, or ejection fraction of \>= 50% by gated radionuclide study * Patients with seizure disorder may be enrolled if on anticonvulsants and well controlled * All patients and/or their parents or legal guardians must sign a written informed consent * All institutional, Food and Drug Administration (FDA), and National Cancer Institute (NCI) requirements for human studies must be met Exclusion Criteria: * Patients who are pregnant or breast-feeding are not eligible for this study; negative pregnancy tests must be obtained in girls who are post-menarchal; males or females of reproductive potential may not participate unless they have agreed to use an effective contraceptive method for the duration of study therapy and for 4 weeks after the last dose of study therapy; breastfeeding women are excluded * Concomitant medications * Corticosteroids: patients requiring corticosteroids who have not been on a stable or decreasing dose of corticosteroid for the 7 days prior to enrollment are not eligible * Patients who have received previous treatment with IMGN901 are not eligible * Investigational drugs: patients who are currently receiving another investigational drug are not eligible * Anti-cancer agents: patients who are currently receiving other anti-cancer agents are not eligible * Anti-graft-versus-host disease (GVHD) or agents to prevent organ rejection post-transplant: patients who are receiving cyclosporine, tacrolimus or other agents to prevent either graft-versus-host disease post bone marrow transplant or organ rejection post-transplant are not eligible for this trial * Patients who have a CNS toxicity \> grade 2 are not eligible * Patients must not have known active central nervous system (CNS) metastases; patients with known central nervous system metastases are excluded unless treated surgically or with radiotherapy, and stable with no recurrent lesions for at least 6 months * Patients who have baseline peripheral neuropathy \>= grade 2 are not eligible * Patients who have an uncontrolled infection are not eligible * Patients who in the opinion of the investigator may not be able to comply with the safety monitoring requirements of the study are not eligible