A First-in-Human Phase I Trial With Antibody Drug Conjugate ADCT-701 in Neuroendocrine Tumors, Carcinomas and Malignant Peripheral Nerve Sheath Tumors

* INCLUSION CRITERIA: * Participants must have histologically or cytologically confirmed neuroendocrine neoplasms or malignant adrenocortical carcinoma (ACC) or malignant peripheral nerve sheath tumors (MPNST). * Locally advanced, unresectable or metastatic disease (as confirmed by a radiological evaluation) * Participants must have measurable disease per RECIST 1.1. * Participants must have received prior standard of care treatment and be refractory to or intolerant to standard of care therapy(s). Note: Patients with MPNST who have refused cytotoxic chemotherapy or for whom treatment on this protocol prior to receiving cytotoxic chemotherapy is felt to be in the best interest for the patient by the local investigator and treating investigator will also be eligible. * Age \>= 18 years. * ECOG performance status \<= 2. * Adequate hematologic function as follows: * Leukocytes \>= 3,000/microliter * Absolute neutrophil count (ANC) \>= 1,200/microliter (off-growth factors for 72 hours prior to treatment initiation) * Hemoglobin (Hgb) \>= 9 g/dL with no blood transfusion within 2 weeks prior to treatment initiation * Platelets \>= 100,000/microliter with no platelet transfusion within 1 week. * Adequate renal and hepatic function as follows: * Creatinine clearance (CrCl) \>= 50 mL/min/1.73 m\^2 (calculated CrCl (Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) or calculated eGFR provided by a laboratory)) * Total bilirubin \<= 1.5 x ULN OR in participants with known or suspected Gilbert's syndrome, total bilirubin \<= 3.0 x ULN * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \<= 2.5 x ULN, (unless liver metastases are present, then values must be \<= 5 x ULN). * Participants serologically positive for hepatitis C virus (HCV) must have an undetectable HCV viral load. * Participants serologically positive for Hepatitis B (HBV) core antibody or surface antigen must be on adequate anti-viral therapy and Hepatitis B Viral deoxyribonucleic acid (DNA) load must be \<2000 IU/mL. * Participants serologically positive for human immunodeficiency virus (HIV) must be on stable antiretroviral therapy for at least 4 weeks before treatment initiation, have no reported opportunistic infections or Castleman s disease within 12 months prior to treatment initiation, have a viral load that is undetectable by quantitative polymerase chain reaction (PCR) and CD4 count \>= 200 cells per cubic millimeter. * Participants with brain metastasis are eligible if at least 4 weeks status post radiotherapy or surgery before treatment initiation with no evidence of progression or associated symptoms. * Individuals of child-bearing potential (IOCBP) must agree to use a highly effective method of contraception (hormonal, intrauterine device (IUD), surgical sterilization) for the duration of the study treatment and up to 9.5 months after the last dose of the ADCT-701 (restriction period). Individuals who can father children must agree to use an effective method of contraception (barrier, surgical sterilization) at study entry and up to 6.5 months after the last dose of the ADCT-701. * Nursing participants must be willing to discontinue nursing from study treatment initiation through 6.5 months after study treatment discontinuation. * Participants or legally authorized representative (LAR) must be able to understand and be willing to sign a written informed consent document. EXCLUSION CRITERIA: * Major surgery, prior treatment with chemotherapy, hormonal therapy, immunotherapy, treatment with an investigational agent, and/or radiation therapy within 4 weeks or 5 half-lives, whichever is shorter, prior to treatment initiation. * Participants taking any herbal supplements within 14 days prior to treatment initiation. * Participants who have wound dehiscence from prior surgeries. * Clinically significant third space fluid accumulation (i.e., ascites requiring drainage or any serosal effusion that is either requires drainage or is associated with shortness of breath) at screening. * Active infection requiring systemic antibiotic therapy at screening. * Active bleeding diathesis or therapeutic anticoagulation with an oral vitamin K antagonist with target international normalized ratio (INR) \> 2 at screening. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to the study drug. * An active autoimmune disease. Note: Participants with type 1 diabetes, eczema, vitiligo, alopecia, psoriasis, hypo- or hyperthyroid disease, adrenal insufficiency on systemic oral corticosteroid therapy (\<= the equivalent of prednisone 10 mg/day), or other mild autoimmune disorders (Type 1 diabetes, eczema, vitiligo, alopecia, rheumatoid arthritis, psoriasis, systemic lupus erythematosus, adrenal insufficiency due to Addison's disease, hypothyroidisms due to Hashimoto's thyroiditis, hyperthyroidisms due to Graves disease, Sjogren s syndrome, celiac disease, pernicious anemia) not requiring immunosuppressive treatment are eligible. * Congenital long QT syndrome, or a corrected QTcF interval of \>=480 ms, at screening (unless secondary to the pacemaker or bundle branch block). * Active second primary malignancy other than non-melanoma skin cancers, nonmetastatic prostate cancer, in situ cervical cancer, ductal or lobular carcinoma in situ of the breast, or other malignancy that does not require current anticancer treatment per standard of care. * Live vaccine administration within 30 days prior to treatment initiation. * Pregnant individuals (confirmed by Beta-Human Chorionic Gonadotropin \[Beta-HCG\] serum or urine pregnancy test) performed at screening. * Uncontrolled intercurrent illness that would limit compliance with study requirements.