Study to Assess the Safety and Tolerability of U3-1565 in Subjects With Advanced Solid Malignant Tumors

Inclusion Criteria: * Pathologically documented advanced solid malignant tumor refractory to standard treatment or for which no standard treatment is available. * Evaluable tumor for all parts of the study and, only for enrollment in Part 2b, measurable tumor per RECIST version 1.1. However, subjects with advanced ovarian cancer may be enrolled in Part 2b even if they do not have a tumor measurable per RECIST version 1.1, as long as they have circulating levels of CA125 higher than 35 U/mL. * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1. * Men or women \>= 18 years of age. * Willing to provide pre-existing diagnostic or resected tumor samples, such as paraffin embedded sections, if available. * Willing, only for enrollment in Part 2b, to provide tumor biopsies before and after treatment. * For female subjects, is postmenopausal (no menstrual period for a minimum of 12 months) or surgically sterile or, if otherwise of childbearing potential, has a negative urine or serum pregnancy test at entry into the study, uses maximally effective birth control during the course of the study, and is willing to use contraception for 6 months following the last study drug administration. * For male subjects, is surgically sterile or willing to use a double barrier contraception method upon enrollment, during the course of the study, and for 6 months following the last study drug administration. * Able to comprehend, sign, and date current Institutional Review Board- (IRB) approved informed consent form (ICF - including Health Insurance Portability and Accountability Act \[HIPAA\] authorization, if applicable) before performance of any study-specific procedures or tests. Exclusion Criteria: * History of lymphoma, leukemia, or other hematopoietic malignancy. * History of human immunodeficiency virus (HIV) positivity. HIV testing is not required for establishing eligibility. * History of bleeding diathesis. * History of idiosyncratic reactions to antibody drug products. * History of stem cell or bone marrow transplant. * History of myocardial infarction (MI) within 6 months before enrollment, symptomatic congestive heart failure (CHF; New York Heart Association \> Class II), unstable angina or unstable cardiac arrhythmia requiring medication * History of clinically significant pulmonary disease after receiving epidermal growth factor receptor- (EGFR) targeting agents. * Any concomitant medical condition that would increase the risk of toxicity, in the opinion of the Investigator or Sponsor. * Clinically active brain metastases defined as symptomatic or requiring treatment with steroids or anti-convulsants. * Unresolved toxicities from prior anti-cancer therapy defined as toxicities, except alopecia, not yet resolved to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) version 4.0 Grade =\< 1 or baseline values. Subjects with chronic Grade 2 toxicities may be eligible at the discretion of the Investigator or Sponsor (eg, Grade 2 chemotherapy-induced neuropathy). * Mean QTcF (Fridericia's correction) intervals \> 450 msec for male subjects and \> 470 msec for female subjects, based on screening electrocardiogram (ECG). * Moderate to severe cardiac valvular abnormalities identified by echocardiography at screening. * Hematological values, as follows: Absolute neutrophil count (ANC) \< 1.5 X 109/L Platelet count \< 100 X 109/L Hemoglobin (Hb) \< 9 g/dL - Renal function, as follows: Creatinine \> 1.5 X upper limit of normal (ULN) or creatinine clearance \< 60 mL/min, as calculated using the modified Cockcroft Gault equation. \- Hepatic function, as follows: Aspartate aminotransferase (AST) \> 3 X ULN (if liver metastases are present, \> 5 X ULN). Alanine aminotransferase (ALT) \> 3 X ULN (if liver metastases are present, \>= 5 X ULN) * Bilirubin \> 1.5 X ULN * Coagulation function, as follows: Prothrombin time (PT) or partial thromboplastin time (PTT) \> 1.5 X ULN * Anti-cancer therapy, including antibody, retinoid, or hormonal treatment, within 3 weeks before enrollment. Prior and concurrent use of hormone replacement therapy, use of gonadotropin-releasing hormone modulators for prostate cancer, and use of somatostatin analogs for neuroendocrine tumors are permitted. * Therapeutic radiation treatment within 4 weeks or palliative radiation treatment within 2 weeks before enrollment, as long as radiation toxicities have resolved to NCI CTCAE grade =\< 1 or baseline values. * Major surgery within 4 weeks before enrollment.