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 creatinine =\< 1.5 x ULN or a calculated creatinine clearance \>= 60 ml/min/1.73 m\^2 (Cockcroft-Gault method) for patients receiving combination of cisplatin and pemetrexed and \>= 45 ml/min/1.73 m\^2 for patients receiving pemetrexed; 24 hour urine for creatinine clearance is acceptable if the calculated creatinine clearance is insufficient * For patients enrolled in Arm B (first stage of phase II of TRC102 and pemetrexed) measurable disease is required according to the Response Evaluation Criteria in Solid Tumors (RECIST) criteria for patients with solid tumors and modified RECIST criteria as described by Byrne and Novak for patients with malignant pleural mesothelioma; pleural effusion and ascites are not considered measurable disease * Patients must be able to swallow whole capsules; nasogastric or gastrointestinal (G)-tube administration is not allowed * The effects of TRC102 on the developing human fetus are unknown; for this reason and because TRC102 as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and 4 months after completion of the study drugs; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately; men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of TRC102, pemetrexed and cisplatin administration; non-childbearing potential is defined as (by other than medical reasons): \>= 45 years of age and has not had menses for \>= 2 years, amenorrheic for \< 2 years without hysterectomy and oophorectomy and a follicle-stimulating hormone value in the postmenopausal range upon pretrial (screening) evaluation, or post hysterectomy, oophorectomy or tubal ligation; documented hysterectomy or oophorectomy must be confirmed with medical records of the actual procedure or confirmed by ultrasound; tubal ligation must be confirmed with medical records of the actual procedure otherwise the patient must be willing to use 2 adequate barrier methods throughout the study, starting with the screening visit though 4 months after the last dose of study drugs * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier; patients who have had targeted therapy will be required to wait 2 weeks due to short half-life of the drugs; treatment with bisphosphonates is permitted * Patients who are receiving any other investigational agents * Patients with active brain metastases or carcinomatous meningitis are excluded from this clinical trial; patients with treated brain metastases, whose brain metastatic disease has remained stable for greater than or equal to 4 weeks without requiring steroid and anti-seizure medications are eligible to participate * History of allergic reactions attributed to compounds of similar chemical or biologic composition to TRC102 or pemetrexed and cisplatin * No studies have been performed to assess potential metabolic and transport interactions of TRC102; as part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product; the case report form must capture the concurrent use of all other drugs, over-the-counter medications, or alternative therapies * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because TRC102 is agent with the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with TRC102, breastfeeding should be discontinued if the mother is treated with TRC102; these potential risks may also apply to other agents used in this study * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with TRC102; in addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy; appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated * Patients with known disorders associated with hemolysis * Patients with thromboembolic disease and on anticoagulation * Patients with a prior cumulative cisplatin dose \> 300 mg/m\^2 (pertains to Arm A only)