Methoxyamine, Cisplatin, and Pemetrexed Disodium in Treating Patients With Advanced Solid Tumors or Mesothelioma That Cannot Be Removed by Surgery or Mesothelioma That Is Refractory to Pemetrexed Disodium and Cisplatin or Carboplatin

Inclusion Criteria: * Arm A dose escalation: patients with histologically or cytologically proven advanced solid tumors for which standard treatments are not available, or for whom the current dose level of cisplatin in combination with pemetrexed is appropriate; =\< 2 prior cytotoxic chemotherapy regimen * Arm A dose level 4 (75 mg/m\^2 cisplatin): patients with histologically proven chemotherapy-naive advanced unresectable solid tumors for which pemetrexed combined with cisplatin is an indicated regimen * Arm B (first stage of phase II of TRC102 and pemetrexed): patients with malignant pleural or peritoneal mesothelioma who had progressed while being treated with or had recurred within 6 months of being treated with pemetrexed and cisplatin or carboplatin frontline; intervening treatment is allowed * Prior pemetrexed is allowed except Arm A dose level 4 (cisplatin 75 mg/m\^2) * Eastern Cooperative Oncology Group (ECOG) performance status 0 -1 (Karnofsky \>= 70%) * Life expectancy of greater than 3 months * Absolute neutrophil count \>= 1,500/uL * Platelets \>= 100,000/uL * Hemoglobin \>= 10.0 g/dl * Prothrombin time or international normalized ratio (INR) =\< 1.5 x upper limit of normal (ULN) * Total bilirubin \< 1.5 x ULN * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional ULN or =\< 5 x ULN if metastatic disease involves liver * Serum …