Nab-Paclitaxel/STI-3031 Complex (AP160-Complex) for the Treatment of Advanced or Metastatic Solid Tumors

Inclusion Criteria: * Provide written informed consent * PRE-REGISTRATION * Age \>= 18 years * Willingness to provide mandatory pre-registration tissue specimen for research * At least one prior systemic therapy in the metastatic setting (adjuvant or neoadjuvant therapy not included). * NOTE: There is no upper limit to the number of prior treatment regimens * Dose Escalation Cohort Only * Patients with histologically or cytologically confirmed advanced or metastatic non-neurological solid tumors, who have no curative or life prolonging therapeutic options * Melanoma Dose Expansion Cohort Only * Histologic proof of surgically unresectable stage IV malignant melanoma * Disease progression on or after anti-PD1/PDL1 antibody-based therapy in the metastatic setting (adjuvant or neoadjuvant therapy with anti-PD1/PDL1 antibody do not count) * REGISTRATION * Tissue submitted for testing at pre-registration shows minimal level of tumor staining for PDL1 (clinical test using 22c3 immunohistochemistry) demonstrating tumor staining in \>= 1% of tumor cells * Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) 0, 1 or 2 * Hemoglobin \>= 9.0 g/dL (patients may be transfused to meet hemoglobin \[Hgb\] requirement) (obtained =\< 14 days prior to registration) * Absolute neutrophil count (ANC) \>= 1500/mm\^3 (obtained =\< 14 days prior to registration) * Platelet count \>= 100,000/mm\^3 (obtained =\< 14 days prior to registration) * Total bilirubin =\< 1.5 x upper li…