More than one line of prior chemotherapy for metastatic or locally advanced disease with the following exception:\r\n* Prior neoadjuvant/adjuvant chemotherapy will not count as line of therapy if completed greater than months prior to initiation of chemotherapy regimen for metastatic or unresectable disease The patient must have experienced disease progression during or within months after the last dose of chemotherapy for metastatic disease, during or within months after the last dose of adjuvant chemotherapy, or have been intolerant of previous chemotherapy Patients must have had at least one prior regimen of systemic chemotherapy for metastatic or locally advanced, unresectable disease; patients must have progressed following the most recent therapy; prior treatment with irinotecan is allowed; for patients that received adjuvant chemotherapy: prior treatment for metastatic disease is not required for patient who experienced disease recurrence during or within months of completion of adjuvant chemotherapy; if the patient received one line of adjuvant treatment and had disease recurrence after months of completing chemotherapy, patients will only be eligible after failing one additional line of chemotherapy used to treat the metastatic or locally advanced, unresectable disease; patients who have received >= lines of systemic chemotherapy for metastatic or locally advanced, unresectable disease are not eligible Progression on at least one prior systemic chemotherapy for advanced, unresectable or metastatic disease; prior adjuvant or neoadjuvant therapy is not included as prior systemic chemotherapy unless treatment occurred within the months prior to study enrollment Patients may have received prior hormone therapy and/or systemic chemotherapy; such therapy must have been completed at least months prior to study entry and the patient has clear evidence of disease subsequent to such therapy; patients must not have received neoadjuvant chemotherapy for the present recurrent disease No prior systemic treatment for unresectable locally advanced or metastatic disease for the tumor type under study. If prior systemic chemotherapy treatment was given in the adjuvant or neo-adjuvant setting or as part of radiotherapy chemotherapy treatment, disease-free interval after stop of systemic treatment must be more than months for non-squamous NSCLC and more than months for UC; Prior chemotherapy:\r\n* History of prior therapy with trastuzumab and a taxane, separately or in combination, is required\r\n* Patients must have either received one line of prior therapy for metastatic breast cancer, or have developed a disease recurrence during or within months after completing adjuvant therapy\r\n* No prior treatment with T-DM is allowed\r\n* Last dose of chemotherapy must be at least days prior to registration For Parts A, B, C, D, E, G and I: Have received prior systemic chemotherapy for metastatic disease. However, the participant may have received prior systemic chemotherapy in the neoadjuvant or adjuvant setting. Histologically confirmed stage IV NSCLC, with no prior systemic anti-cancer therapy of any kind (including EGFR and ALK inhibitors), prior definitive chemoradiation for locally advanced disease is permitted as long as the last administration of chemotherapy or radiation (whichever was given last) occurred at least months prior to enrollment; prior adjuvant or neoadjuvant chemotherapy for early stage lung cancer is permitted if completed at least months prior to initiating study treatment Patients may not have received prior systemic treatment (chemotherapy or targeted therapy) for advanced BTC; prior adjuvant chemotherapy is permitted provided it was completed > months from registration Patients must have failed or are intolerant to one line of systemic treatment but no more than prior lines of systemic chemotherapy for advanced BTC; patients who received adjuvant chemotherapy and had evidence of disease recurrence within months of completion of the adjuvant treatment are also eligible; if the patient received adjuvant treatment and had disease recurrence after months, patients will only be eligible after failing or having intolerance to one line of systemic chemotherapy used to treat the disease recurrence Patients may have received adjuvant chemotherapy and up to two prior chemotherapy for metastatic or locally recurrent disease; no prior nab-paclitaxel or mifepristone therapy for metastatic disease will be allowed Have received at least prior systemic therapy in the metastatic or unresectable disease setting; patients who have recurred within six months of adjuvant chemotherapy are not required to have received an additional line of chemotherapy Prior chemotherapy for metastatic CRPC; prior neoadjuvant chemotherapy or chemotherapy for metastatic hormone sensitive prostate cancer are allowed so long as this treatment was completed at least months prior to initiation of sipuleucel-T Phase I and expansion cohort: Up to two prior non-taxane chemotherapy regimens for metastatic disease are permitted for patients enrolled on the phase I portion of the trial; patients with HER/neu positive breast cancer are not eligible; patients treated with prior anthracycline therapy as neoadjuvant, adjuvant, or metastatic therapy are not eligible unless the following conditions are met: (a) prior cumulative doxorubicin dose is =< mg/m^ (or epirubicin dose is =< mg/m^), and (b) left ventricular ejection fraction (LVEF) obtained at baseline is at least % (or >= % above lower institutional limits of normal whichever is higher); patients with estrogen receptor (ER)-positive disease are required to have relapse or progression on at least one line of endocrine therapy No prior chemotherapy for inoperable locally advanced or mUC. For patients who received prior adjuvant/neoadjuvant chemotherapy or chemo-radiation for urothelial carcinoma, a treatment-free interval > months between the last treatment administration and the date of recurrence is required in order to be considered treatment naive in the metastatic setting Only one line of prior systemic treatment for metastatic urothelial cancer. Participants who received neoadjuvant or adjuvant chemotherapy and showed disease progression (as defined above), within months of the last dose are considered to have received systemic chemotherapy in the metastatic setting Cohort : prior chemotherapy and anti-PD(L) [in combination or in maintenance setting] (anti-PD(L) alone is allowed only for participants with documented cisplatin ineligibility) and Cohort : prior chemotherapy (no prior anti-PD(L) treatment) Must have received at least two one prior line of therapy for mCRPC; a taxane chemotherapy administered for metastatic castration sensitive disease will not count, unless patient develops disease progression within months from the last dose chemotherapy No prior systemic cancer therapy for recurrent or metastatic disease (except if chemotherapy was part of multimodal treatment completed months prior to enrolment). No prior chemotherapy for metastatic/recurrent disease; prior adjuvant or neo-adjuvant treatment with a fluoropyrimidine or fluoropyrimidine based regimen is allowed only if it is completed at least months prior to the start of study drug, whether given alone or with radiation therapy; patients who have received prior neo-adjuvant therapy (chemotherapy and/or radiation therapy) which did not contain fluorouracil (-FU) or capecitabine and have been diagnosed with metastatic disease (with no previous treatment in the metastatic setting) are eligible; no -month window is required for these patients; in the setting of metastatic disease requiring local palliation, only radiosensitizing doses of -FU or capecitabine monotherapy are permitted Subjects who have documented disease recurrence within months of completing neoadjuvant or adjuvant chemotherapy for limited disease will be eligible for study; subjects who recur greater than months after completing adjuvant chemotherapy will not be eligible unless they receive additional chemotherapy for advanced disease In dose escalation, patients must have had at least one prior line of chemotherapy for advanced disease or progressed within months of adjuvant therapy (prior chemotherapy and/or anti-EGFR therapy is permitted) Prior neoadjuvant or adjuvant systemic therapy or local intravesical chemotherapy or immunotherapy is permitted if such therapy was completed at least months prior to the initiation of study treatment and if all toxicities from such therapy have improved to grade or stabilized or resolved The subject has demonstrated radiographic progression after front-line treatment for locally advanced or metastatic disease (prior adjuvant therapy allowed if >= months elapsed between end of adjuvant therapy and metastatic relapse) Patients who received adjuvant or neoadjuvant platinum-doublet chemotherapy (after surgery and/or radiation therapy) and developed recurrent or metastatic disease within months of completing therapy are not excluded. No prior chemotherapy for locally advanced or metastatic urothelial cancer\r\n* Perioperative chemotherapy previously administered in the neoadjuvant and/or adjuvant setting is permitted\r\n* Prior chemotherapy administered in the context of chemoradiation as definitive treatment for bladder preservation is also permitted, provided that disease progression outside the prior radiotherapy field is demonstrated histologically or cytologically Subjects must have previously untreated metastatic colorectal cancer and have no contraindications to treatment with the standard of care regimen as determined by the investigator; prior adjuvant therapy is acceptable (including immunotherapy), but must have been completed at least months prior to metastatic disease diagnosis Patients who received prior taxane-based chemotherapy as neoadjuvant or adjuvant therapy for local disease, or who received taxane-based therapy in the PSA clinical (non-metastatic) state is allowable provided that the total duration of exposure was six cycles or less and chemotherapy was completed more than months prior to registration Previous disease progression on or intolerance to one line of therapy either platinum-based or immunotherapy (pembrolizumab or nivolumab); prior chemotherapy in the induction, organ preservation, definitive or adjuvant setting permitted if it was for initial treatment of locally advanced or metastatic disease and completed more than months prior to enrollment on the current study; -week washout period prior to treatment start will be required At least prior systemic therapy for metastatic disease; adjuvant chemotherapy or concurrent chemoradiation for early stage disease does not count as prior therapy unless patients progressed within months of completion of chemotherapy Patients must satisfy the following criteria for prior therapy:\r\n* Progressed on and following at least months of combined treatment with palbociclib and AI therapy for advanced/metastatic breast cancer, and be able and willing to receive additional palbociclib treatment; palbociclib and AI must be the most recently received treatment prior to enrollment; up to one () prior line of chemotherapy for advanced/metastatic disease is allowed in addition to any number of prior lines of endocrine therapy\r\n* No prior treatment with fulvestrant, everolimus, or any agent whose mechanism of action is to inhibit the PIK-mTOR pathway in the metastatic setting; use of these agents in the neoadjuvant and/or adjuvant settings is permitted\r\n* Patients receiving bisphosphonate therapy prior to registration may continue at the same intervals used prior to study registration INCLUSION CRITERIA FOR TNBC: Patients must have received standard adjuvant, neoadjuvant, and/or metastatic chemotherapy per National Comprehensive Cancer Network (NCCN) or institutional practice; no maximum on number of prior systemic treatment regimens Patients may have received prior systemic chemotherapy; such therapy must have been completed at least years prior to study entry and the patient has no evidence of disease subsequent to such therapy; patients must not have received neoadjuvant chemotherapy for the present disease Randomized phase II: be treatment naive in the stage IV setting; subjects who received platinum-containing adjuvant, neoadjuvant or definitive chemoradiation therapy given for locally advanced disease, and developed recurrent (local or metastatic) disease < months of completing therapy are ineligible for this arm; subjects with recurrent disease >= months after completing a platinum-containing adjuvant, neoadjuvant or definitive chemoradiation therapy given for locally advanced disease, who also subsequently progressed during or after a systemic regimen given to treat the recurrence, are eligible for this arm At least one prior regimen for treatment of recurrent or metastatic disease\r\n* Note: Prior regimen for recurrent or metastatic disease is not required if the patient had disease progression or recurrence during or within the first months following completion of adjuvant or neoadjuvant chemotherapy Histologic or cytological diagnosis of SQCLC with advanced/metastatic stage, with no known curative treatment options; prior platinum-containing adjuvant, neoadjuvant, or definitive chemoradiation therapy given for locally advanced disease is considered first line therapy only if recurrent (local or metastatic) disease developed within months of completing therapy; subjects with recurrent disease > months will be eligible Must have received at least one but no more than lines of chemotherapy for advanced breast cancer\r\n* Patients who have developed metastatic disease on adjuvant hormone therapy within months of completing adjuvant chemotherapy are considered to have had one line of chemotherapy and are eligible for this trial ARM A COHORT : Patients must not have received prior therapy for metastatic or advanced disease; adjuvant therapy that is gemcitabine based is allowed as long as the adjuvant treatment was completed >= months before the diagnosis of recurrent disease ARM C COHORT : Patients must not have received prior systemic chemotherapy for advanced or metastatic disease; prior adjuvant chemotherapy or concurrent chemotherapy and radiation are allowed if they were completed >= months prior to the diagnosis of recurrent disease Any prior adjuvant cytotoxic chemotherapy within months of registration; subjects who received chemotherapy for earlier stage disease more than months prior to study registration are eligible for this trial Patients with prior oral or intravenous chemotherapy for metastatic disease\r\n* Patients may have had adjuvant or neoadjuvant chemotherapy, if therapy was completed more than months prior to enrollment\r\n* Patients whose comorbidities prevent them from being able to receive the designated chemotherapy regimen\r\n* Patients who are assigned to receive epirubicin must have cardiac ejection fraction (EF) of % or greater Stage I: subjects may have already received no more than cycle of their platinum-based chemotherapy but should not have received other prior chemotherapy regimens with the exception of patients with metastatic disease who received neoadjuvant or adjuvant chemotherapy and that chemotherapy was completed > months prior to enrollment Stage II: subjects must have received no more than prior chemotherapy regimen for metastatic disease; and no more than cycles of their current platinum chemotherapy regimen for metastatic disease; they must have recovered to < grade from all toxicities related to the prior chemotherapy; patients who have received perioperative (i.e. adjuvant or neoadjuvant therapy) > year prior to being treated with chemotherapy for metastatic disease will be eligible provided any chemotherapy-related toxicity has recovered to specified levels Subject has received prior systemic chemotherapy for locally advanced unresectable or metastatic gastric or GEJ adenocarcinoma. However, subject may have received either neo-adjuvant or adjuvant chemotherapy as long as it was completed at least months prior to the first dose of study treatment. Have had no prior systemic chemotherapy for metastatic disease; at least months since prior adjuvant chemotherapy. Additional Inclusion Criteria for Cohort : Patients must have received at least one prior chemotherapy regimen for metastatic disease\r\n* NOTE: Patients who received anthracycline and taxane containing adjuvant or neoadjuvant therapy and progressed within months may enter this trial as their first therapy for metastatic breast cancer (MBC) Patients who have metastatic or recurrent disease after previous surgery, radiation therapy, and/or chemotherapy are eligible. In Stage , no restriction is placed on the number of prior therapies. In Stage , patients may have or prior chemotherapy treatments for adjuvant or metastatic disease and no prior endocrine therapies. Patients may not have received prior systemic chemotherapy for metastatic/advanced urothelial carcinoma; note: prior neoadjuvant/adjuvant therapy is permitted if completed >= months prior to registration for protocol therapy; prior intravesical therapy is permitted Received prior systemic cytotoxic chemotherapy or investigational agent(s), excluding EGFR TKIs, for metastatic NSCLC. [Notes: ) Prior treatment with chemotherapy and/or radiation as part of neoadjuvant/adjuvant therapy is allowed as long as therapy was completed at least months prior to the diagnosis of metastatic NSCLC. ) If participant received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting study treatment. ) Prior exposure to traditional medicine(s) is allowed as long as therapy was discontinued at least weeks prior to the first dose of study treatment.] Cholangiocarcinoma cohort specific criteria:\r\n* Patients must have histologically or cytologically documented carcinoma primary to the intra- or extra-hepatic biliary system or gall bladder with clinical and/or radiologic evidence of unresectable, locally advanced or metastatic disease; patients with ampullary carcinoma are not eligible\r\n* Patients must have failed at least one (but no more than ) prior line of systemic therapy in the advanced disease setting\r\n* Patients who received adjuvant chemotherapy and had evidence of disease recurrence within months of completion of the adjuvant treatment are also eligible; in this case, the adjuvant therapy will count as the minimum required one prior line of therapy; if patient received adjuvant treatment and had disease recurrence after months, patients will only be eligible after failing one regimen of systemic chemotherapy used to treat the (unresectable or metastatic) disease recurrence\r\n* If the patient has had decompression of the biliary tree within the last days, stability of the bilirubin level needs to be confirmed with two measurements that are within to days of each other; (the second measurement must be obtained within days prior to registration); both the first and second measurement must be =< . x IULN; stability is defined as the second measurement being no more than one point higher than the first For patients with locally advanced disease, no previous radiotherapy, surgery, chemotherapy, or investigational therapy for the treatment of PDAC is permitted; for patients with metastatic disease, prior treatment for non-metastatic disease with -fluorouracil (-FU) or gemcitabine administered as radiation sensitizer, or as a cytotoxic therapy, in the adjuvant setting is allowed, provided at least months have elapsed since completion of the last dose and no >= grade treatment-related toxicities are present Prior therapy: Eligible subjects must have had line of systemic cytotoxic treatment; this may be adjuvant therapy with documented progression within months of completion, or line of cytotoxic therapy for metastatic disease; NOTE: eligible patients are allowed up to lines of systemic cytotoxic treatment, of which only line is allowed for metastatic disease; the acceptance of progression within months of adjuvant is part inclusion to not require patient to re-challenge with chemotherapy (chemo) if they progressed soon after adjuvant therapy; prior hormonal therapy for metastatic/recurrent disease is also allowed; prior targeted therapy not directed against cMET or vascular endothelial growth factor (VEGF) pathways is allowed Relapsed after or refractory to one or two prior lines of chemotherapy for advanced or metastatic/recurrent disease (at least one cycle each) which have not included a PD-L or FGFR inhibitor; at least one regimen should have included a platinum agent unless contraindicated for the subject; prior neoadjuvant or adjuvant chemotherapy (without a PD-L or FGFR inhibitor) is permitted and will not be counted as first-line chemotherapy, as long as the subject has not progressed within months of the last dose; however, a regimen of neoadjuvant or adjuvant chemotherapy will be counted as first-line chemotherapy if the patient progressed within months of the last dose Up to prior chemotherapy regimens for recurrent disease are allowed; adjuvant chemotherapy and maintenance Taxol after completion of six cycles of adjuvant carboplatin - Taxol will not be counted as a \prior chemotherapy regimen\ for the purpose of this study; treatment with targeted agents or hormones would not be considered as a systemic chemotherapy regimen; eligible Patients are those with documented disease recurrence/progression within - months of completing platinum-based chemotherapy; patients should not have received any non-oncology, viral vaccines within days prior to starting protocol treatment No more than one prior systemic therapeutic regimen for unresectable stage III or stage IV melanoma; this includes chemotherapy, biologic therapy, biochemotherapy, or investigational treatment; this does not include any therapies given in the adjuvant setting; however, patients are excluded if they have a history of prior treatment for melanoma (either adjuvant or metastatic disease) with ipilimumab or other cytotoxic T-lymphocyte antigen (CTLA-) inhibitor, or prior interferon-alpha treatment for metastatic disease (history of adjuvant interferon-alpha is allowed); there should be a -week washout period between last treatment administration and initiation of study therapy Prior conventional cytotoxic chemotherapy for metastatic or recurrent disease; prior adjuvant, neoadjuvant or chemoradiotherapy for NSCLC is permitted, provided at least months elapsed prior to documented metastatic recurrence No prior chemotherapy for the treatment of metastatic disease at study entry. Adjuvant chemotherapy is permitted providing cytotoxic chemotherapy was completed months prior to starting the study and without disease recurrence. Previous therapy for locally advanced, unresectable or metastatic gastric/GEJ cancer. Participant may have received prior neoadjuvant or adjuvant therapy as long as it was completed at least months prior to randomization Use of taxanes as adjuvant therapy or to treat locally advanced disease is permitted, if given more than months prior to CD- First-line locally advanced and/or metastatic breast cancer with no prior adjuvant chemotherapy unless the Investigator determines that one of the cytotoxic chemotherapy agents in the control arm would otherwise be offered to the subject Subjects must have received no previous chemotherapy or investigational therapy for the treatment of metastatic disease. Adjuvant, neo-adjuvant chemotherapy or chemoradiotherapy is permitted providing cytotoxic chemotherapy was completed > months prior to randomization, without disease recurrence or progression during those months. Participants may have received - prior chemotherapeutic regimens for metastatic breast cancer and must have been off treatment with chemotherapy for at least days prior to registration; no prior platinum in the metastatic setting is allowed; prior platinum in the neo/adjuvant setting is permissible, if at least months elapsed since the end of adjuvant therapy to the development of metastatic disease; all toxicities related to prior chemotherapy must have resolved to Common Terminology Criteria for Adverse Events (CTCAE) version (v) . grade or lower; if a patient recurs within months of neoadjuvant or adjuvant chemotherapy, this will be counted as one line of therapy for metastatic disease Metastatic disease with documented disease progression following previous treatment with at least one, but no more than prior therapies, with one of the prior therapies having been either gemcitabine-based or fluoropyrimidine-based therapy. Neoadjuvant and/or adjuvant therapies for localized resectable or unresectable PDAC each count as a line of therapy if multiagent chemotherapy regimens were administered (and neoadjuvant regimen was different than adjuvant regimen) and if the participant progressed with metastatic disease while taking or within months of completion of (neo)adjuvant therapy. For Part B - Subjects must not have received any prior systemic treatment for metastatic MCC. Prior chemotherapy treatment in the adjuvant setting (no clinically detectable disease; no metastatic disease) is allowable if the end of treatment occurred at least months prior to study start) Group B Phase : No prior systemic treatment for advanced or metastatic disease (adjuvant and/or neoadjuvant therapies are allowed if completed at least months prior to study entry. No prior tyrosine kinase inhibitor therapy is allowed at any time prior to study entry) Have received previous chemotherapy for advanced NSCLC. Participants who have received adjuvant or neoadjuvant chemotherapy are eligible if the last administration of the prior regimens occurred at least year prior to study entry. Progression on at least one prior systemic chemotherapy for advanced, unresectable or metastatic disease; prior adjuvant or neoadjuvant therapy is not included as prior systemic chemotherapy unless treatment occurred within the months prior to study enrollment\r\n* There is no limit to the number of prior lines of treatment a patient has received\r\n* No treatment with biologic therapy, immunotherapy, chemotherapy, investigational agent for malignancy, or radiation =< days before study registration; no treatment with nitrosourea or mitomycin =< days before study registration\r\n* Patients should have resolution of any toxic effects of prior therapy (except alopecia) to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE), version ., grade or less Patients must have had one or two prior regimens of systemic chemotherapy for metastatic or locally advanced, unresectable disease; (a maintenance regimen of -fluorouracil or capecitabine, with or without bevacizumab, should not be counted as a separate line of treatment); prior treatment with irinotecan is allowed; prior treatment for metastatic disease is not required for patients who experienced disease recurrence during or within months of completion of adjuvant chemotherapy Prior Therapy:\r\n* No more than two regimens in the metastatic setting as long as patients have adequate performance status; patients with no prior chemotherapy for metastatic disease may be included in the trial if they received anthracyclines and taxanes in the adjuvant or neoadjuvant settings; chemotherapy nave patients with metastatic disease must have failed anthracyclines and taxanes\r\n* Chemotherapy treatment prior to enrollment must be discontinued for at least weeks prior to study entry\r\n* Patients must have completed radiation therapy at least days prior to beginning protocol treatment Has received systemic therapy for the treatment of their stage IV NSCLC. Completion of treatment with chemotherapy and/or radiation as part of neoadjuvant/adjuvant therapy is allowed as long as therapy was completed at least months prior to the diagnosis of metastatic disease. Subjects who received platinum-containing adjuvant, neoadjuvant or definitive chemoradiation therapy given for locally advanced disease, and developed recurrent (local or metastatic) disease within months of completing therapy are eligible Patients may have had prior adjuvant treatment for colorectal cancer; the prior treatment regimen must not have included bevacizumab but may have included oxaliplatin and the last dose of chemotherapy must have been > months prior to study entry; patients with prior radiotherapy are acceptable; it must be at least weeks since administration of radiation therapy and all signs of toxicity must have abated Prior chemotherapy or immunotherapy for metastatic urothelial bladder cancer; prior neoadjuvant or adjuvant chemotherapy with first progression > months is allowed Have had no prior systemic therapy for advanced or metastatic disease. Prior adjuvant therapy should have been completed at least months from documentation of metastatic disease. Prior palliative radiotherapy allowed if toxicities resolved to grade or baseline. No prior systemic chemotherapy for metastatic disease (adjuvant or neoadjuvant platinum-based chemotherapy with recurrence > months since completion of therapy is allowed) Have received and failed only prior chemotherapy regimen for metastatic pancreatic cancer\r\n* Must have received and failed only prior regimen administered for pancreatic cancer in the metastatic setting; failure includes development of metastases on or within months of adjuvant chemotherapy treatment or development of metastases on or within months of treatment for locally advanced disease or radiographic disease progression on or within months of treatments for metastatic disease; documented intolerance (grade or toxicity or hospitalization leading to discontinuation) of treatment for metastatic disease will also be considered a failure\r\n* Radiosensitizing doses of chemotherapy are not considered systemic chemotherapy Patients are allowed to have had a maximum of prior chemotherapy regimen for metastatic disease; patients are allowed to have a maximum of two prior regimens if they previously received neoadjuvant/adjuvant chemotherapy or chemoradiotherapy for their initial localized disease Patients must not have received prior systemic therapy for their advanced cancer; prior intravesical therapy completed weeks prior to enrollment and adjuvant/neoadjuvant chemotherapy completed more than months prior to diagnosis of advanced disease are permitted Patients must have failed no more than prior line of systemic chemotherapy for advanced biliary cancer; patients who received adjuvant chemotherapy and had evidence of disease recurrence within months of completion of the adjuvant treatment are also eligible; if patient received adjuvant treatment and had disease recurrence after months, patients will only be eligible after failing one line of systemic chemotherapy used to treat the disease recurrence Must have completed preoperative (neoadjuvant) chemotherapy. NOTE: Acceptable preoperative regimens include an anthracycline or a taxane, or both. Participants who received preoperative therapy as part of a clinical trial may enroll. Participants may not have received adjuvant chemotherapy after surgery prior to randomization. Bisphosphonate use is allowed. No treatment with prior taxane-based chemotherapy for metastatic disease\r\n* Patients who received prior taxane-based chemotherapy as neoadjuvant or adjuvant therapy for local disease, or who received taxane-based therapy in the PSA clinical (non-metastatic) state is allowable provided that the total duration of exposure was six cycles or less and chemotherapy was completed more than months prior to registration\r\n* Taxane-based chemotherapy that was aborted due to allergic reactions or intolerance to chemotherapy and therefore received cycle of prior therapy is allowable Participants must have received at least line of chemotherapy for advanced or metastatic breast cancer and/or relapse/progressed while on or within months of completion of neoadjuvant or adjuvant trastuzumab/pertuzumab; prior pertuzumab is allowed for Cohort B but not Cohort A Up to one prior line of chemotherapy for advanced disease is allowed; if received, prior chemotherapy must be discontinued at least days prior to initiation of protocol therapy Prior therapy for NSCLC that may include surgery, radiation therapy, immunotherapy and/or ? prior chemotherapy regimens (such as neoadjuvant/adjuvant treatment), however only chemotherapy regimen in the metastatic setting is allowed. No prior systemic treatment for advanced or metastatic colorectal cancer is allowed; prior regional chemotherapy (e.g., hepatic arterial infusion) is also not allowed; patients may have received previous neoadjuvant or adjuvant chemotherapy and/or chemoradiation per institutional standard of care; the last course of adjuvant therapy must have been concluded > months prior to colorectal cancer recurrence Subjects must have previously untreated locally advanced or metastatic pancreatic adenocarcinoma; patients newly diagnosed with metastatic recurrence after history of adjuvant therapy for resected disease are eligible, if completion of adjuvant therapy was greater than months ago Patients must have had one prior systemic chemotherapeutic regimen for management of advanced, metastatic, or recurrent carcinoma of the cervix\r\n* Chemotherapy administered concurrent with primary radiation (e.g.; weekly cisplatin) is not counted as a systemic chemotherapy regimen for management of advanced, metastatic, or recurrent disease; adjuvant chemotherapy given following the completion of radiation therapy (or concurrent chemotherapy and radiation therapy) is not counted as a systemic chemotherapy regimen for management of advanced, metastatic, or recurrent disease (e.g.; paclitaxel and carboplatin for up to cycles) More than prior antineoplastic treatment regimens (excluding hormonotherapy) for metastatic disease. Subjects who relapsed under adjuvant treatment shouldn't have received more than one line of chemotherapy for metastatic disease (part only). Patients may have received no prior chemotherapy for metastatic or unresectable disease; patients may have received prior adjuvant therapy (chemotherapy and/or chemoradiation) if more than months have elapsed between the end of adjuvant therapy and registration; patients may not have received prior docetaxel or cisplatin No prior systemic chemotherapy for patients who present with metastatic disease. For patients with recurrent head and neck squamous cell carcinoma, prior chemotherapy is allowed if it was given as part of their definitive therapy. If patients have received prior combined modality therapy, they must be off therapy for at least months. Subject has received intervening anticancer treatment or previous treatment with chemotherapy for metastatic disease other than palliative local radiation to painful bone metastases completed at least week prior to the first dose of study drug. The administration of neoadjuvant or adjuvant chemotherapy is allowed as long as it has finalized ? months before the first dose of study drug. Prior therapies:\r\n* Patients may have received one line of non-gemcitabine containing chemotherapy regimen\r\n* Patients may have received prior adjuvant chemotherapy and/or radiation therapy greater than months prior to the time of study enrollment\r\n* Patients may have received maintenance therapy, e.g. lower dose capecitabine after completion of adjuvant therapy; this will not be considered as therapy for metastatic disease AND will patients may have been on maintenance therapy within the months prior to initiating gemcitabine plus nab-paclitaxel, i.e. right up until the initiation of first-line therapy for metastatic disease\r\n* Timing of prior therapies:\r\n** At least days must have passed since all prior anti-cancer therapy, including chemotherapy, biological therapy, or radiation therapy, and any prior investigational agent\r\n** However, at least days must have passed since any prior antibody-based therapies (such as, but not limited to cetuximab or bevacizumab)\r\n** All patients must have completely recovered from all transient side effects related to prior therapies\r\n*** However, any side effects that are expected to be more durable or even permanent (e.g., neurotoxicity or ototoxicity) must have resolved to at least grade Prior treatment with cytotoxic chemotherapy for advanced NSCLC; neoadjuvant/adjuvant chemotherapy is permitted if at least months has elapsed between the end of chemotherapy and randomization Received prior chemotherapy regimen for advanced or metastatic disease (not including neoadjuvant and/or adjuvant therapy). No prior therapy for metastatic disease except \r\n* For Group A: > months since completion of adjuvant chemotherapy\r\n* For Group B: those patients who enroll just after completing bevacizumab plus either FOLFOX or FOLFIRI Subjects with histologically confirmed stage IV or recurrent NSCLC (per the th International Association for the Study of Lung Cancer classification squamous or nonsquamous histology, with no prior systemic anticancer therapy (including EGFR and ALK inhibitors) given as primary therapy for advanced or metastatic disease\r\n* Prior adjuvant or neoadjuvant chemotherapy is permitted as long as the last administration is at least months prior to enrollment\r\n* Prior definitive chemoradiation for locally advanced disease is also permitted as long as the last administration of chemotherapy or radiotherapy (whichever was given last) occurred at least months prior to enrollment No previous radiotherapy, chemotherapy or investigational therapy for the treatment of metastatic disease. Prior treatment with -FU or gemcitabine administered as a radiation sensitizer in the adjuvant setting is allowed, provided at least months have elapsed since completion of the last dose and no lingering toxicities are present. Prior treatment with taxanes if given as full-dose chemotherapy for advanced disease; as neoadjuvant therapy, taxanes cannot be used in months prior to enrollment Received only prior systemic chemotherapy regimen for Stage IIIb, IV, or recurrent disease not including neoadjuvant and/or adjuvant therapy. (NOTE: Exceptions may be allowed based on prior treatment regimens and tumor types in agreement with protocol requirements.) No prior systemic chemotherapy or WEE kinase inhibitor therapy for metastatic or recurrent disease will be allowed; patients are permitted to have received prior systemic chemotherapy as a part of the initial multimodality treatment for locally advanced disease if this treatment was completed more than months prior to enrollment Received up to prior chemotherapy regimens (not including neoadjuvant/adjuvant therapy) for advanced or metastatic disease Received prior chemotherapy regimen for advanced or metastatic disease (not including neoadjuvant and/or adjuvant therapy). Patients who have received more than two prior lines of antineoplastic therapy for advanced disease. Chemotherapy administered as neoadjuvant or adjuvant treatment more than six months prior to study enrollment is not considered a prior line of therapy for purposes of this study. Patient's nave to first-line therapy for the advanced stage of the disease. Previous neoadjuvant or adjuvant therapy is allowed for patients who successfully underwent complete radical surgery and if last treatment was administered more than months prior to the start of the study treatment, i.e., D of Cycle . For urothelial cancer patients, no prior combination systemic chemotherapy for metastatic disease, except:\r\n* Single-agent radiosensitizing chemotherapy is not considered prior systemic therapy\r\n* Prior neoadjuvant or adjuvant systemic chemotherapy (including cisplatin-based) is allowed provided it was completed >= months prior to the diagnosis of metastatic disease\r\n* Prior intravesical therapy is permitted No prior anti-cancer therapy for the treatment of metastatic disease at the time of signing the ICF. Adjuvant treatment is permitted providing cytotoxic chemotherapy was completed months prior to signing the ICF and without disease recurrence. Previous chemotherapy for locally advanced or metastatic gastric carcinoma (adjuvant or neoadjuvant chemotherapy must be completed at least months prior to randomization) Has received systemic therapy for the treatment of advanced stage NSCLC. Completion of treatment with chemotherapy and/or radiation as part of neoadjuvant/adjuvant therapy is allowed as long as therapy was completed at least months prior to the diagnosis of metastatic disease Prior systemic therapy (including chemotherapy, biological or hormonal therapy) will be permitted for palliative treatment of metastatic or unresectable relapsed disease; additionally, previous chemotherapy delivered with curative-intent (i.e., chemoradiotherapy or adjuvant [postoperative] chemotherapy at a time disease was considered potentially curable) will be permitted; prior taxane (including paclitaxel or docetaxel) and/or platinum exposure will be permitted; however, patients must not have experienced disease progression within months of platinum-based therapy; at least weeks must have elapsed since prior chemotherapy or radiation therapy, weeks if the last regimen included carmustine (BCNU) or mitomycin C; toxicities from prior anticancer therapy must have recovered to =< grade Patient may not have previously received chemotherapy for metastatic disease, except adjuvant therapy completed at least months before the first evidence of metastasis Patients with metastatic disease who are eligible for first line FOLFOX chemotherapy. Adjuvant or neoadjuvant given at least months prior for non-metastatic disease is permitted. Prior systemic chemotherapy for cholangiocarcinoma or gallbladder carcinoma; NOTE: adjuvant chemotherapy is allowed if completed > months prior to the start of registration Phase II: Patient who recurs with metastatic disease =< months of completing adjuvant chemotherapy after curative-intent surgical resection is not eligible; patients who recur with metastatic disease > months after completion of adjuvant chemotherapy are eligible Prior chemotherapy for metastatic breast cancer (MBC) (prior adjuvant chemotherapy permitted as long as > months [mo]) Subjects who have either received chemotherapy for metastatic disease or are considered by the treating investigator to be appropriate candidates for chemotherapy as current treatment for metastatic breast cancer are excluded. Chemotherapy administered for adjuvant/neo adjuvant disease is acceptable provided it was administered at least year prior to study entry. Patients must have received at least one prior therapy for unresectable disease; patients with recurrence within months of completion of neoadjuvant or adjuvant therapy may be considered as having received one prior therapy for unresectable disease Patients must be planning to receive one of the study-allowed regimens as their initial treatment for their current disease; myelosuppressive therapy must follow the standard regimen, although a dose reduction of up to % is permitted; this treatment may be neoadjuvant or adjuvant chemotherapy; patients must not be receiving or planning to receive concurrent radiation during systemic treatment For participants who received prior adjuvant/neoadjuvant chemotherapy or chemo-radiation for urothelial carcinoma, a treatment-free interval more than (>) months between the last treatment administration and the date of recurrence is required in order to be considered treatment naive in the metastatic setting Histologically or cytologically confirmed diagnosis of advanced or recurrent (Stage IIIB not amenable for multimodality treatment) or metastatic (Stage IV) NSCLC that is ALK-positive by an FDA-approved assay performed centrally. Patients must be ALK positive by local test prior to submitting tissue to the central lab. Randomization will occur after ALK positive confirmation is received from the central lab. Patients may have received up to prior chemotherapy regimen for metastatic disease, which may also include maintenance therapy. Note that patients that have received adjuvant or neoadjuvant chemotherapy and developed metastatic disease within months from the end of that therapy would be considered to have received prior regimen for metastatic disease.