Known hypersensitivity to afatinib, cisplatin, or pemetrexed
Disease progression after treatment with at least one line of chemotherapy that included a platinum agent in combination with pemetrexed
Subjects treated with pemetrexed (pemetrexed disodium) previously will be eligible only if  weeks have elapsed between the last dose of pemetrexed and the date of surgery
Patients who have been treated with pemetrexed if the last dose of pemetrexed is <  weeks to the date of surgery
Part B only: Participants must have malignant pleural or peritoneal mesothelioma and appropriate candidate for treatment with cisplatin/pemetrexed; no prior systemic chemotherapy
Patients must have had at least one prior chemotherapy regimen that includes pemetrexed and cisplatin or carboplatin; there is no limit to the number of prior chemotherapy regimens received
Must be fit enough to receive next-line chemotherapy (either gemcitabine, docetaxel, or pemetrexed [non-squamous only]) according to the discretion of the treating physician
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; =<  prior cytotoxic chemotherapy regimen
Arm A dose level  ( mg/m^ cisplatin): patients with histologically proven chemotherapy-naive advanced unresectable solid tumors for which pemetrexed combined with cisplatin is an indicated regimen (malignant mesothelioma, non-small cell lung cancer, ovarian cancer and thymoma)
Arm B (first stage of phase II of TRC and pemetrexed): patients with malignant pleural or peritoneal mesothelioma who had progressed while being treated with or had recurred within  months of being treated with pemetrexed and cisplatin or carboplatin frontline; intervening treatment is allowed
Prior pemetrexed is allowed except Arm A dose level  (cisplatin  mg/m^)
Patients will have received at least  cycles of induction chemotherapy with pemetrexed/cisplatin or pemetrexed/carboplatin
Patient must have prior treatment with a platinum plus pemetrexed regimen
Patients who had received at least  prior therapies for advanced or metastatic disease condition, including platinum doublet and pemetrexed, docetaxel, or immunotherapy, and were refractory to or unable to tolerate their last prior therapy
Patients must have had at least one prior chemotherapy regimen that includes pemetrexed and cisplatin or carboplatin; there is no limit to the number of prior chemotherapy regimens received
Subjects must be considered suitable for chemotherapy with either single-agent pemetrexed or docetaxel.
Known or presumed intolerance of pemetrexed or sorafenib
For NSCLC participants in parts C, D, and F: if currently receiving gemcitabine or pemetrexed (single-agent or in combination with another therapy), a participant may continue to receive  of these  therapies provided that extracranial disease is stable for at least  weeks and CNS disease progression has occurred while on this therapy.
Have received more than  previous lines of cytotoxic chemotherapy (if receiving cisplatin, -FU or pemetrexed)
Patients must have histologically or cytologically confirmed malignant mesothelioma for which they have received pemetrexed in combination with cisplatin as part of chemotherapeutic regimen.
Patients must not have received any other chemotherapeutic treatment for malignant mesothelioma other than pemetrexed and a platinum agent such as cisplatin.
Known sensitivity to any component of cisplatin, carboplatin, or pemetrexed.
No prior treatment with systemic anti-EGFR inhibitors or pemetrexed is permitted
Known sensitivity to any component of cisplatin, carboplatin or pemetrexed.
Has mesothelioma (pleural, peritoneal, pericardial, tunica vaginalis) of any histology that is relapsed or refractory after treatment with at least one pemetrexed-containing regimen
No more than  prior lines of anti-cancer therapy, one of which must have included pemetrexed and a platinum.
Peritoneal mesothelioma basket \r\n* Refractory or intolerant to platinum and pemetrexed systemic therapy\r\n* Any number of prior therapies
Received at least one prior pemetrexed-based chemotherapy for unresectable disease, unless within  months of receiving platinum-pemetrexed therapy for neoadjuvant or adjuvant treatment that has been unsuccessful
For Part A (abemaciclib + pemetrexed): Non-squamous subtypes only. The participant must have received at least one but no more than three prior therapies for advanced/metastatic NSCLC.
Disease progression on or after pemetrexed and cis- or carboplatin
No more than  prior lines of cytotoxic therapy, which should have included pemetrexed and a platinum
At least one prior line of systemic therapy including platinum and pemetrexed
Prior treatment with pemetrexed <  months prior to starting study drug
Subjects who received any prior treatment with docetaxel are excluded. Subjects who have received gemcitabine in first line therapy but do not have squamous cell carcinoma, will be eligible as they can receive pemetrexed for the salvage regimen.
CRIZOTINIB PLUS PEMETREXED ARM B, PAXOPANIB PLUS PEMETREXED ARM C, CRIZOTINIB PLUS PAZOPANIB PLUS PEMETREXED ARM D:
Prior therapy with pemetrexed
Inability to discontinue non-steroidal anti-inflammatory drugs for  days (long half-life) or for  days (short half-life, if CrCL < mL/min) before pemetrexed dosing and until  days after pemetrexed dosing
Patients with unresectable, malignant pleural or peritoneal mesothelioma who have progressed on first-line pemetrexed-based chemotherapy
Therapy that does not include cisplatin, carboplatin, gemcitabine, and/or pemetrexed
. Received only one prior chemotherapy regimen consisting of ?  cycles of pemetrexed/cisplatin or pemetrexed/carboplatin; subjects must have documentation of an ongoing response (confirmed PR or SD) following completion of this regimen. Subjects changing from cisplatin to carboplatin or vice versa within the same course of treatment because of platinum toxicity will be considered to have had first-line chemotherapy. Note: Subjects may have undergone previous surgical resection of their disease providing it was completed prior to initiation of chemotherapy.
Planned to receive  to  cycles of pemetrexed or gemcitabine in combination with cisplatin or carboplatin  For subjects to receive pemetrexed, planned to receive vitamin B and folate per pemetrexed approved labeling
Participants who have received prior Pemetrexed treatment.
Patient with a history of severe hypersensitivity reaction to the planned study treatment including gemcitabine, paclitaxel, cisplatin, carboplatin, pemetrexed or any known excipients of these drugs
Pemetrexed/cisplatin therapy; note: patients who will receive pemetrexed/cisplatin therapy must meet all eligibility criteria below:\r\n* Patients assigned to pemetrexed/cisplatin therapy must NOT have squamous cell histology\r\n* Calculated creatinine clearance must be obtained within  weeks of registration and calculated creatinine clearance (CrCl) must be >= mL/min using the standard Cockcroft and Gault formula, or the measured glomerular filtration rate (GFR) using the appropriate radiolabeled method (-CrEDTA or Tcm-DTPA) must be used to calculate CrCl