Patients must not have any co-existing condition that would preclude full compliance with the study; no prior history of severe hypersensitivity reaction to docetaxel or other drugs formulated with polysorbate 80Xx_NEWLINE_xXPrevious chemotherapy with at least 3 cycles of docetaxel for hormone-sensitive metastatic prostate cancerXx_NEWLINE_xXAny prior chemotherapy or androgen receptor (AR)-directed therapy for CRPC, (e.g. docetaxel, cabazitaxel, mitoxantrone, abiraterone acetate, ketoconazole, or enzalutamide); previous treatment with radium-223 or sipuleucel-T is allowedXx_NEWLINE_xXPrior history of allergic reactions to docetaxel and/or to medications formulated with polysorbate 80Xx_NEWLINE_xXMay have received treatment with abiraterone acetate, enzalutamide and/or one prior chemotherapy (docetaxel)Xx_NEWLINE_xXPrior treatment with docetaxel within 6 months of study enrollmentXx_NEWLINE_xXKnown hypersensitivity to the components of MM-310, or docetaxelXx_NEWLINE_xXtaxanes (paclitaxel or docetaxel) or epirubicin,Xx_NEWLINE_xXDocetaxel monotherapy is a reasonable treatment in the judgement of the InvestigatorXx_NEWLINE_xXA known history of allergy to docetaxel, Cremophor or polysorbate 80 (Tween 80)Xx_NEWLINE_xXPrior use of abiraterone acetate, enzalutamide, docetaxel, cabazitaxel, carboplatin, or radium-223 for the treatment of castration-resistant disease\r\n* Prior docetaxel use in the hormone-sensitive disease setting is allowed, but must be completed >= 4 weeks prior to enrollment\r\n* Prior sipuleucel-T use is allowed, but must be completed >= 4 weeks prior to enrollment\r\n* Concurrent use of zolendronic acid or denosumab is allowed on studyXx_NEWLINE_xXRadiosensitizing chemotherapy (taxol [paclitaxel], taxotere [docetaxel], cisplatin, gemcitabine [gemcitabine hydrochloride], 5-fluorouracil [fluorouracil]) given within one week of radiation treatmentXx_NEWLINE_xXPrior systemic chemotherapy (docetaxel, cabazitaxel, estramustine, other cytotoxic agents)Xx_NEWLINE_xXPrior treatment with docetaxel chemotherapy in the castration-resistant setting. Prior treatment with docetaxel in either the neoadjuvant or adjuvant setting or for hormone sensitive disease (e.g., CHAARTED population) is allowed, as long as therapy was completed > 12 months prior to study registrationXx_NEWLINE_xXAgree to use barrier methods of birth control during the docetaxel portion of the protocol and for at least one month after last docetaxel administrationXx_NEWLINE_xXAny previous exposure to docetaxelXx_NEWLINE_xXPrior docetaxel for hormone-sensitive prostate cancer is permitted if =< 6 doses were given in conjunction with first-line androgen deprivation therapy and > 12 months since last dose of docetaxelXx_NEWLINE_xXPrior treatment with docetaxel or cabazitaxel for metastatic castration-resistant prostate cancer is prohibitedXx_NEWLINE_xXAny therapy including chemotherapy (e.g., docetaxel) or biological therapy (e.g., vaccine, immunotherapy) for the treatment of castration-resistant prostate cancer. Previous treatment with flutamide, steroidal anti-androgens, androgens, estrogens, bicalutamide, nilutamide, or 5-? reductase inhibitor is permitted.Xx_NEWLINE_xXAssigned by the physician to receive either docetaxel or immune checkpoint inhibitor per standard of care regimensXx_NEWLINE_xXPatients planned to receive docetaxel with contra-indications to receive docetaxelXx_NEWLINE_xXHistory of allergic reaction to docetaxelXx_NEWLINE_xXPrevious treatment with docetaxel for metastatic prostate cancerXx_NEWLINE_xXHistory of known hypersensitivity to cetuximab, docetaxel or similar agentsXx_NEWLINE_xXHas received any prostate cancer directed chemotherapy in the castration resistant setting. Subjects who have received up to 6 prior doses of docetaxel in the castration sensitive setting are permitted if they have not experienced disease progression within 36 weeks of last treatment with docetaxelXx_NEWLINE_xXHas known grade >= 3 docetaxel-related toxicities or docetaxel toxicity related dose interruption or discontinuationXx_NEWLINE_xXPatients who have had chemotherapy for metastatic castration-resistant prostate cancer within the past year (patients who have had docetaxel for metastatic castration sensitive per CHAARTED data may enroll as long as they did not have progressive disease while on docetaxel and are 6 months removed from treatment, with all treatment related toxicities resolving to at least grade 1)Xx_NEWLINE_xXChemotherapy naive (prior docetaxel chemotherapy [as per chemohormonal therapy versus androgen ablation randomized trial for extensive disease (CHAARTED) data] for castration sensitive disease is allowed)Xx_NEWLINE_xXPrior chemotherapy (e.g. docetaxel, cabazitaxel) for CRPC; prior docetaxel administered in the castrate-sensitive space is allowedXx_NEWLINE_xXPrior treatment with ADI-PEG 20, gemcitabine, or docetaxelXx_NEWLINE_xXThe participant has received prior treatment with gemcitabine or docetaxel. Note: Participants previously enrolled in the I5B-MC-JGDJ (NCT02451943) or any other blinded study with olaratumab are not eligible to participate in this trial.Xx_NEWLINE_xXCandidates for ADT and docetaxel. Started ADT with or without first generation anti androgen, but no longer than 12 weeks before randomizationXx_NEWLINE_xXPrior systemic chemotherapy (docetaxel, cabazitaxel, estramustine, other cytotoxic agents)Xx_NEWLINE_xXPrior taxane-based chemotherapy with progressive disease on chemotherapy\r\n* Prior docetaxel for metastatic hormone sensitive prostate cancer is allowed, if no progression of disease on docetaxel as defined by RECIST v1.1 and PCWG3\r\n* Prior taxane-based chemotherapy (i.e. docetaxel or cabazitaxel with or without platinum agent) for mCRPC is allowed if no progression of disease on chemotherapy as defined by RECIST v1.1 and PCWG3Xx_NEWLINE_xXDocetaxel appropriate\r\n* Patients who have not received prior docetaxel (or other taxane therapy) in the advanced setting are eligible for all cohorts\r\n* Patients who have previously received docetaxel (or other taxane therapy) in the advanced setting are eligible for the dose escalation cohort only, if anticipated to have maintained taxane sensitivity and in the opinion of the investigator would still benefit from further docetaxel therapyXx_NEWLINE_xXDOSE ESCALATION COHORT: Prior receipt of docetaxel is permittedXx_NEWLINE_xXPHARMACODYNAMIC EXPANSION COHORT: Prior receipt of docetaxel is not permittedXx_NEWLINE_xXDISEASE SPECIFIC EXPANSION COHORTS: Prior receipt of docetaxel is not permittedXx_NEWLINE_xXPrevious cytotoxic chemotherapy including cisplatin, carboplatin, oxaliplatin, etoposide, docetaxel, cabazitaxel, and gemcitabine is allowed, up to 3 prior regimensXx_NEWLINE_xXPrior exposure to docetaxel, selinexor, or another selective inhibitor of nuclear transport (SINE) compoundXx_NEWLINE_xXMust be fit enough to receive next-line chemotherapy (either gemcitabine, docetaxel, or pemetrexed [non-squamous only]) according to the discretion of the treating physicianXx_NEWLINE_xXHas had any previous exposure to paclitaxel or docetaxel in the last 5 years.Xx_NEWLINE_xXHave received at least 4 cycles of docetaxel or cabazitaxel, and less than ten, with two consecutive rising PSA values, checked at least 7 days apartXx_NEWLINE_xXRadiographic progressive disease, irrespective of PSA changes, after receiving at least 4 cycles of docetaxel or cabazitaxelXx_NEWLINE_xXDocetaxel: Creatinine clearance no minimumXx_NEWLINE_xXReceived more than 10 cycles of docetaxel (for docetaxel cohort only) or 6 of cabazitaxel (for cabazitaxel cohort only)Xx_NEWLINE_xXLast docetaxel or cabazitaxel dose > 6 weeks prior to enrollmentXx_NEWLINE_xXProgressive disease, both docetaxel naive and docetaxel treated.Xx_NEWLINE_xXLess than 6 weeks since last myelosuppressive therapy (including Docetaxel, Cabazitaxel, 223Ra, 153Sm) or other radionuclide therapy.Xx_NEWLINE_xXPrior exposure to a taxane (paclitaxel or docetaxel)-based regimen in localized or advanced/metastatic setting.Xx_NEWLINE_xXPatients with a history of allergic reactions attributed to docetaxel or paclitaxel are ineligibleXx_NEWLINE_xXPrior docetaxel as first line therapy in addition to androgen deprivation is allowedXx_NEWLINE_xXPrior treatment with chemotherapy (docetaxel or cabazitaxel) for castration resistant prostate cancerXx_NEWLINE_xXA minimum of 4 weeks from prior chemotherapy, including but not limited to, docetaxel, cabazitaxel, mitoxantrone, carboplatin, cisplatin, or estramustine; if applicable, prior to registrationXx_NEWLINE_xXPatient has received enzalutamide for the treatment of prostate cancer; however, previous treatment with other hormonal therapy (bicalutamide, abiraterone, ketoconazole, flutamide, and nilutamide) or chemotherapy (docetaxel, cabazitaxel, or mitoxantrone) is allowedXx_NEWLINE_xXPrevious treatment with docetaxel or an Axl inhibitorXx_NEWLINE_xXPatients who had received at least 2 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 therapyXx_NEWLINE_xXHistologically confirmed metastatic castrate resistant cancer (mCRPC) who progressed after both hormonal therapy (abiraterone or enzalutamide) and chemotherapy (docetaxel, for example); or cannot tolerate either or both of these classes of therapies.Xx_NEWLINE_xXPatient has received niclosamide, abiraterone or ketoconazole for the treatment of prostate cancer; however, previous treatment with other hormonal therapy (bicalutamide, enzalutamide, flutamide and nilutamide) or chemotherapy (docetaxel, cabazitaxel or mitoxantrone) is allowedXx_NEWLINE_xXmCRPC EXPANSION COHORT: Patients must have received prior treatment with enzalutamide and/or abiraterone with the exception of patients who were treated with docetaxel and androgen deprivation therapy for metastatic castrate-sensitive prostate cancer and progressed on docetaxel treatment or who progress within one month of the last docetaxel doseXx_NEWLINE_xXmCRPC EXPANSION COHORT: Patients who were treated for metastatic castrate-sensitive prostate cancer with docetaxel and androgen deprivation therapy who progress on docetaxel treatment or who progress within one month of the last docetaxel dose are eligibleXx_NEWLINE_xXReceived any prior treatment with any taxane (docetaxel or paclitaxel) for small cell lung cancerXx_NEWLINE_xXPrior or ongoing systemic therapy for prostate cancer including, but not limited to:\r\n* Hormonal therapy (e.g. leuprolide, goserelin, triptorelin)\r\n* Cytochrome P450 (CYP)-17 inhibitors (e.g. abiraterone, ketoconazole)\r\n* Antiandrogens (e.g. bicalutamide, nilutamide)\r\n* Second generation antiandrogens (e.g. enzalutamide)\r\n* Immunotherapy (e.g. sipuleucel-T, ipilimumab)\r\n* Chemotherapy (e.g. docetaxel, cabazitaxel)Xx_NEWLINE_xXSubjects must be considered suitable for chemotherapy with either single-agent pemetrexed or docetaxel.Xx_NEWLINE_xXNSCLC that is predominantly squamous cell carcinoma, and patient had docetaxel as part of his prior chemotherapy.Xx_NEWLINE_xXPatients with squamous cell histology or non-squamous cell histology previously treated by pemetrexed and with a contraindication for docetaxel with grade ? 2 neuropathy or hypersensitivity reaction to medications formulated with polysorbate 80 (Tween 80) as they could be randomly assigned to Arm B.Xx_NEWLINE_xXPrior therapy with abiraterone, enzalutamide and/or docetaxel; there is no limit to the number of prior treatment regimensXx_NEWLINE_xXPrior adjuvant chemotherapy with gemcitabine and/or docetaxel/paclitaxel is allowedXx_NEWLINE_xXPrior therapy with abiraterone, enzalutamide and/or docetaxel; if a patient has not received docetaxel or cabazitaxel chemotherapy, the patient must be informed of this treatment choice as an alternative; if the patient has received docetaxel or cabazitaxel chemotherapy or refuses one of both of these therapies, this rationale must be documented and the patient is then eligible; patient must be offered and made aware of all Food and Drug Administration (FDA)?approved treatment options; patients with bone only disease may not have received radium-223Xx_NEWLINE_xXPrior cytotoxic chemotherapy (for example, but not limited to, docetaxel, mitoxantrone, cabazitaxel) within 6 months of registration is prohibitedXx_NEWLINE_xXARM B COHORT 2: Patients must not have prior exposure to docetaxelXx_NEWLINE_xXARM B COHORT 3: Patients must not have prior exposure to docetaxelXx_NEWLINE_xXPHASE II STUDY METASTATIC CASTRATE-RESISTANT PROSTATE CANCER COHORT 4 ELIGIBILITY CRITERIA (MEDI+O ONLY):\r\nPatients must have received prior treatment with enzalutamide and/or abiraterone with the exception of patients who were treated with docetaxel and androgen deprivation therapy for metastatic castrate-sensitive prostate cancer and progressed on docetaxel treatment or who progress within one month of the last docetaxel doseXx_NEWLINE_xXPHASE II STUDY METASTATIC CASTRATE-RESISTANT PROSTATE CANCER COHORT 4 ELIGIBILITY CRITERIA (MEDI+O ONLY):\r\nPatients who were treated for metastatic castrate-sensitive prostate cancer with docetaxel and androgen deprivation therapy who progress on docetaxel treatment or who progress within one month of the last docetaxel dose are eligibleXx_NEWLINE_xXPatients with hypersensitivity to docetaxel or polysorbate 80 (Arm A only)Xx_NEWLINE_xXPrior treatments with Cyp 17 inhibitors like TAK-700/orteronel, ketoconazole, radium 223 or docetaxel (up to 6 cycles of docetaxel given in the non CRPC setting is allowed); prior treatment with sipuleucel-T is allowedXx_NEWLINE_xXGreater than 2 prior therapies in metastatic CRPC (including single-agent docetaxel, abiraterone); abiraterone can only be taken pre-chemotherapyXx_NEWLINE_xXTo commence third line docetaxel, patients must have grade 2 or less neuropathy from prior oxaliplatin treatment; also bilirubin > upper limit of normal (ULN), or AST and/or ALT > 1.5 x ULN concomitant with alkaline phosphatase > 2.5 x ULN are not eligible for docetaxel therapyXx_NEWLINE_xXPrior docetaxel for hormone-sensitive prostate cancer is permitted if =< 6 doses were given in conjunction with first-line androgen deprivation therapy and > 12 months since last dose of docetaxelXx_NEWLINE_xXPrior treatment with docetaxel or cabazitaxel for metastatic castration-resistant prostate cancer is prohibitedXx_NEWLINE_xXPatients who have had prior therapy with gemcitabine or docetaxelXx_NEWLINE_xXPatients with known hypersensitivity to gemcitabine or docetaxelXx_NEWLINE_xXPatients who have received the combination of gemcitabine and docetaxel in the metastatic setting are excludedXx_NEWLINE_xXAny history of severe hypersensitivity reaction to docetaxel or other drugs formulated with polysorbate 80Xx_NEWLINE_xXPatients with a history of severe hypersensitivity reaction to docetaxel or other drugs formulated with polysorbate 80. Please refer to Study Appendix O for a complete list of Polysorbate 80 containing drugs.Xx_NEWLINE_xXHas hypersensitivity to pembrolizumab, docetaxel or any of its excipientsXx_NEWLINE_xXKnown hypersensitivity to docetaxel or other drugs formulated with polysorbate 80Xx_NEWLINE_xXPrior therapy with docetaxelXx_NEWLINE_xXPatients previously treated with docetaxel for NSCLC or with known severe hypersensitivity to taxane therapies.Xx_NEWLINE_xXNo prior chemotherapy for the treatment of mCRPC; patients may have received docetaxel for the treatment of hormone-sensitive prostate cancerXx_NEWLINE_xXPrior therapy with sipuleucel-T, abiraterone, enzalutamide, docetaxel, and/or cabazitaxel; there is no limit to the number of prior treatment regimens, so long as prior therapy does not include platinum chemotherapy or a PARP inhibitorXx_NEWLINE_xXPrior therapy with a MEK-inhibitor or docetaxel for metastatic non-small cell lung cancer (docetaxel in the adjuvant setting will be allowed)Xx_NEWLINE_xXNo prior abiraterone acetate, enzalutamide or apalutamide or other novel AR or CYP17 antagonist, or docetaxel for castration resistant prostate cancer; if used for hormone naïve disease, last dose was at least 12 months prior to randomizationXx_NEWLINE_xXMore than one prior taxane regimen at any stage of the disease under study (“taxane” refers to paclitaxel, docetaxel, abraxane and cabazitaxel); adjuvant and/or neoadjuvant treatments are considered together as one prior regimenXx_NEWLINE_xXNo prior docetaxel or cabazitaxel chemotherapy for metastatic castration-resistant prostate cancer (mCRPC) (men treated with prior docetaxel administered as up-front therapy with androgen deprivation therapy [ADT] > 6 months ago will be eligible); prior abiraterone is allowedXx_NEWLINE_xXPrior treatment with docetaxel or cabazitaxel for mCRPCXx_NEWLINE_xXPatient has received enzalutamide for the treatment of prostate cancer; however, previous treatment with other hormonal therapy (bicalutamide, flutamide, nilutamide, abiraterone and ketoconazole) or chemotherapy (docetaxel, cabazitaxel or mitoxantrone) is allowedXx_NEWLINE_xXPrior treatment with docetaxel.Xx_NEWLINE_xXPatients must have progressed on Arm 2 (docetaxel) of this sub-studyXx_NEWLINE_xXPatients must have progressed on Arm 2 (docetaxel) of this sub-studyXx_NEWLINE_xXPatients must have progressed on Arm 2 (docetaxel) of this sub-studyXx_NEWLINE_xXPrior treatment with docetaxel is allowed but not requiredXx_NEWLINE_xXPatients who are deemed to have high-risk or extensive metastatic, hormone sensitive prostate cancer (mHSPC) per “clinical judgment” of the treating physician are eligible for enrollment if they are unsuitable candidates for docetaxel or if they have declined docetaxel therapyXx_NEWLINE_xXEligible for treatment with a taxane-containing regimen (for example, docetaxel), unless taxane-containing regimen was declined after an informed decisionXx_NEWLINE_xXPrior chemotherapy (for example, docetaxel, cabazitaxel) for treatment of CRPC, except when docetaxel has been given for hormone-sensitive prostate cancerXx_NEWLINE_xXSubjects who are not indicated for chemotherapy treatment with first line Standard of Care chemotherapy (docetaxel and prednisone)Xx_NEWLINE_xXFor Cohort A: Has received docetaxel for mCRPC. Prior treatment with 1 other chemotherapy for mCRPC is allowed. Up to 2 second-generation hormonal manipulations (e.g., abiraterone acetate and/or enzalutamide) are allowedXx_NEWLINE_xXFor Cohort B: Has received prior treatment with docetaxel or another chemotherapy agent for metastatic prostate cancerXx_NEWLINE_xXFor Cohort C: Has received prior chemotherapy for mCRPC. Prior docetaxel for metastatic hormone-sensitive prostate cancer is allowed if ?4 weeks elapsed from last dose of docetaxelXx_NEWLINE_xXPatients who have had prior therapy with docetaxel, gemcitabine hydrochloride, or doxorubicin hydrochloride at any time in their historyXx_NEWLINE_xXPatients with a history of severe hypersensitivity reaction to Taxotere (docetaxel) or other drugs formulated with polysorbate 80Xx_NEWLINE_xXUp to 6 cycles of docetaxel therapy with final treatment administration completed within 2 months of day 1 and no evidence of disease progression during or after the completion of docetaxel therapy;Xx_NEWLINE_xXUp to 6 months of ADT with LHRH agonists or antagonists or orchiectomy with or without concurrent antiandrogens prior to day 1 if subject was treated with docetaxel, with no radiographic evidence of disease progression or rising PSA levels prior to day 1;Xx_NEWLINE_xXParticipants who received docetaxel treatment must meet the following criteria: a) Received a maximum of 6 cycles of docetaxel therapy for mHSPC; b) Received the last dose of docetaxel <=2 months prior to randomization; c) Maintained a response to docetaxel of stable disease or better, by investigator assessment of imaging and PSA, prior to randomizationXx_NEWLINE_xXTaking any other systemic anticancer agent (docetaxel, doxorubicin, irinotecan)Xx_NEWLINE_xXPatients with prior grade 3 allergic or infusion reactions to docetaxel, cisplatin or cetuximab are not eligible; a history of well tolerated infusion reactions is NOT an exclusionXx_NEWLINE_xXHave not received prior treatment with docetaxel.Xx_NEWLINE_xXPatients must either not be a candidate for docetaxel chemotherapy for newly diagnosed metastatic prostate cancer, as determined by their treating oncologist, or have declined this therapyXx_NEWLINE_xXPatients who have disease progression during, or after, receiving docetaxel and have had at least 12 weeks of treatment and in the opinion of the investigator are unlikely to derive significant benefit from additional docetaxel-based therapy, or were intolerant to therapy with this agent.Xx_NEWLINE_xXPatients who have received more than 2 prior non-docetaxel containing cytotoxic chemotherapy regimens for Metastatic Castration-Resistant Prostate Cancer (mCRPC).Xx_NEWLINE_xXPrior therapy with docetaxel for NSCLCXx_NEWLINE_xXParticipant has a known sensitivity to docetaxel or other drugs formulated with polysorbate 80Xx_NEWLINE_xXBe eligible for treatment with physician's choice of comparator treatment (abiraterone acetate, enzalutamide or docetaxel)Xx_NEWLINE_xXPrior treatment with any of the chemotherapy medications (cisplatin or docetaxel) for HNSCC or with AZD1775Xx_NEWLINE_xXPrior cytotoxic chemotherapy for prostate cancer, but up to 2 cycles of docetaxel chemotherapy for metastatic disease is permitted.Xx_NEWLINE_xXHas rapid progression of visceral disease and, thus is a candidate for docetaxel; this determination will be at the discretion of the treating physicianXx_NEWLINE_xXHistory of severe hypersensitivity reaction to paclitaxel, docetaxel, or to other drugs formulated with polysorbate 80 or polyoxyethylated castor oil, or to vinflunine or other vinca alkaloidsXx_NEWLINE_xXHistory of severe hypersensitivity reaction (>= grade 3) to docetaxelXx_NEWLINE_xXPreviously received docetaxel or are not healthy enough per clinical judgment or declined to receive itXx_NEWLINE_xXPrior cytotoxic chemotherapy with the exception of docetaxel or cabazitaxel; treatment with docetaxel or cabazitaxel must be discontinued >= 4 weeks from the time of enrollment, and recovery of adverse events (AEs) to grade 1 or baseline (however, ongoing neuropathy is permitted)Xx_NEWLINE_xXPatients must have one of the following a) low volume disease (defined as no visceral metastases and < 4 bone metastases) or b) are not candidates for docetaxel based chemotherapy or c) refused docetaxel chemotherapyXx_NEWLINE_xXPrior treatment with eribulin, fulvestrant or anastrozole, paclitaxel, abraxane, docetaxel, vinorelbine, or capecitabineXx_NEWLINE_xXFor the randomised phase only, patients must have received chemotherapy in the form of docetaxel treatment for metastatic castration-resistant prostate cancer. Note: patients who discontinued docetaxel for toxicity reasons and without completing the full course will still be eligible to enter this study provided they received at least 2 cycles of chemotherapy.Xx_NEWLINE_xXPrior disease progression on docetaxel or paclitaxel in metastatic settingXx_NEWLINE_xXHistory of allergic reaction to docetaxelXx_NEWLINE_xXParticipants may have received prior docetaxel-based chemotherapy for prostate cancer; such chemotherapy must have been stopped at least three weeks prior to the first dosing in this studyXx_NEWLINE_xXPatients who have had chemotherapy for metastatic castration-resistant prostate cancer; (patients who have had docetaxel for metastatic castration sensitive disease per ChemoHormonal Therapy Versus Androgen Ablation Randomized Trial for Extensive Disease in Prostate Cancer [CHAARTED] Data may enroll as long as they did not have progressive disease while on docetaxel and are 6 months removed from treatment, will all treatment related toxicities resolving to at least grade 1)Xx_NEWLINE_xXHistory of allergic reactions attributed to compounds of similar chemical or biologic composition to docetaxel or tryptophan containing substances. This would include L-tryptophan or 5-hydroxy-tryptophan supplements. Also patients with a history of severe hypersensitivity reactions to docetaxel or to other drugs formulated with polysorbate 80 are excluded.Xx_NEWLINE_xXTreatment with a single course of gefitinib(Iressa®) or erlotinib (Tarceva®), or other small molecule or targeted therapies, or monoclonal antibody therapy (excluding docetaxel) will be considered and count as prior chemotherapy.Xx_NEWLINE_xXSubjects 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.Xx_NEWLINE_xXPrior cytotoxic chemotherapy (e.g. docetaxel, mitoxantrone, cabazitaxel) within 6 months of registration is prohibitedXx_NEWLINE_xXThe subject has had treatment with docetaxel for the treatment of metastatic castrate-sensitive prostate cancer within 6 months before the first dose of study treatmentXx_NEWLINE_xXThe subject has had progression of prostate cancer during 6 cycles of prior docetaxel treatment for castrate sensitive diseaseXx_NEWLINE_xXPrior treatment with DocetaxelXx_NEWLINE_xXPrior therapy with pazopanib, gemcitabine or docetaxel; patients who have had prior treatment with gemcitabine or docetaxel for a prior malignancy are eligible if they meet the criteria in exclusion #3 and did not experience significant drug related toxicityXx_NEWLINE_xXAny concern for hypersensitivity to pazopanib, gemcitabine or docetaxelXx_NEWLINE_xXE 16. History of hypersensitivity to docetaxel, or polysorbate 80.Xx_NEWLINE_xXPlanned or recent initiation of standard docetaxel therapy; patients may be enrolled after receiving standard docetaxel therapy as long as the patient has not demonstrated evidence of progression for more than 45 days before enrollment (“late enrollers”)Xx_NEWLINE_xXKnown hypersensitivity to docetaxel, fluorouracil (5-FU)Xx_NEWLINE_xXPatients who have received previous docetaxel or cisplatinXx_NEWLINE_xXPatients with rapidly progressive disease who are candidates for other approved therapies such as docetaxel, abiraterone, and enzalutamide.Xx_NEWLINE_xXPrior treatment with docetaxel-based chemotherapyXx_NEWLINE_xXNo known hypersensitivity to any of the following agents: oxaliplatin, cisplatin, capecitabine, 5-flurouracil, docetaxel, or irinotecanXx_NEWLINE_xXPrior treatment with docetaxel within 6 months of enrollmentXx_NEWLINE_xXSubject has been previously treated with enzalutamide for at least 8 months, and stopped enzalutamide due to progressive disease (not due to adverse events), followed by at least 4 cycles of docetaxel and/or cabazitaxel chemotherapy, with or without other intervening anti-cancer therapies (including but not limited to aminoglutethimide, ketoconozole, abiraterone acetate, Rad-223, or sipuleucel-T), prior to receiving chemotherapy. Note: for patients who receive sequential taxanes, there must not have been progressive disease upon ending the first taxane, or use of any anti-cancer agents between the two taxanes.Xx_NEWLINE_xXPrevious treatment with docetaxel.Xx_NEWLINE_xXHypersensitivity to the active substance or ingredients of PEGPH20 and docetaxel.Xx_NEWLINE_xXReceived prior treatment with docetaxel.Xx_NEWLINE_xXPatients who require or may be expected to require urgent treatment with docetaxel during the study (e.g., patients with visceral metastases).Xx_NEWLINE_xXPatients receiving chemotherapy (e.g., docetaxel, cabazitaxel, taxane, or platinum as single agents or in combination) as their cancer treatmentXx_NEWLINE_xXPrior cytotoxic chemotherapy, immunotherapy, a PI3K/AKT/mTOR agent (including TORC1 and TORC2 inhibitors), or RA 223 dichloride for the treatment of castration resistant prostate cancer (CRPC). Participants may have received docetaxel in the hormone-sensitive setting.Xx_NEWLINE_xXPatient must be eligible for chemotherapy with docetaxelXx_NEWLINE_xXOngoing systemic therapy (other than a GnRH agonist/antagonist) for prostate cancer including, but not limited to:\r\n* CYP-17 inhibitors (e.g. ketoconazole, abiraterone)\r\n* Antiandrogens (e.g. bicalutamide, nilutamide)\r\n* Second generation antiandrogens (e.g. enzalutamide)\r\n* Immunotherapy (e.g. sipuleucel-T, ipilimumab)\r\n* Chemotherapy (e.g. docetaxel, cabazitaxel)\r\nNote: Prior receipt of these agents is acceptable; no washout period is requiredXx_NEWLINE_xXPrior treatment with trastuzumab emtansine, docetaxel, or paclitaxel either as single\n             agents or as part of a treatment regimen.Xx_NEWLINE_xXPatients who have had prior sipuleucel-T, docetaxel, cabazitaxel, abiraterone or enzalutamide as a single agent, or in combination therapyXx_NEWLINE_xXSymptomatic patients who, in the opinion of the investigator, may benefit from docetaxel-based chemotherapyXx_NEWLINE_xXPrior treatment with docetaxel or mogamulizumab;Xx_NEWLINE_xXPrior treatment with docetaxelXx_NEWLINE_xXA single course of gemcitabine and/or docetaxel as adjuvant therapy that was completed at least 6 months prior to planned first doseXx_NEWLINE_xXPrior docetaxel or other chemotherapy for mCRPC; patients who have received docetaxel for metastatic hormone-sensitive prostate cancer are eligibleXx_NEWLINE_xXPatients in whom urgent treatment with docetaxel is indicated, per clinician discretion; this includes, but is not limited to patients with symptomatic visceral metastatic diseaseXx_NEWLINE_xXPrior treatment with MLN4924; however, prior treatment with docetaxel, paclitaxel, and carboplatin is allowed.Xx_NEWLINE_xXPrior treatment with docetaxel for recurrent or advanced NSCLCXx_NEWLINE_xXPrior treatment with docetaxel-containing therapyXx_NEWLINE_xXPrior treatment with MLN4924; however, prior treatment with docetaxel, paclitaxel,carboplatin, and gemcitabine is allowedXx_NEWLINE_xXHistory of severe hypersensitivity reactions to docetaxel (polysorbate 80-based formulations) for patients to be enrolled in Arm 1 (MLN4924 + docetaxel), history of hypersensitivity to carboplatin for patients to be enrolled in Arm 2 (MLN4924 + paclitaxel + carboplatin), or history of severe hypersensitivity to paclitaxel (cremophor-based formulations) for patients to be enrolled in Arm 2Xx_NEWLINE_xXParticipants with NSCLC to be treated with docetaxel need to have received at least one prior anti-cancer treatment regimen in an advanced setting and to have docetaxel be considered appropriate treatmentXx_NEWLINE_xXReceived prior docetaxel chemotherapyXx_NEWLINE_xXPart 2 only: Patients must be docetaxel-naive.Xx_NEWLINE_xXPart 2 only: Patients may not have had prior treatment with docetaxel.Xx_NEWLINE_xXHistory of treatment with docetaxel in any setting. Participants treated with prior paclitaxel are eligible.Xx_NEWLINE_xXPregnant women and breast feeding women are excluded from this study because of the risk to a fetus due to docetaxel chemotherapy and OGX-427 systemic treatment (fertility toxicology studies have not been completed for OGX-427).Xx_NEWLINE_xXUp to 6 patients with castration-resistant prostate cancer (CRPC) that was pathologically confirmed as adenocarcinoma of the prostate and with evidence of metastatic disease on bone scan or other imaging. Patient must have progressive disease after at least one hormonal treatment and one cytotoxic therapy e.g. with docetaxel, mitoxantrone.Xx_NEWLINE_xXPrior treatment with docetaxel-based chemotherapyXx_NEWLINE_xXPatients who have received docetaxel plus anti-androgen therapy (ADT) for metastatic castrate sensitive prostate cancer are eligible for the study; (patients may enroll as long as they did not have progressive disease while on docetaxel and are 6 months removed from treatment, with all treatment related toxicities resolving to at least grade 1)Xx_NEWLINE_xXHave had treatment with docetaxel for the treatment of metastatic castrate-sensitive prostate cancer within 6 months before the first dose of study enrollmentXx_NEWLINE_xXHave had progression of prostate cancer on prior docetaxel treatment for castrate sensitive diseaseXx_NEWLINE_xXPatients with a history of severe hypersensitivity reaction to docetaxel or other drugs formulated with polysorbate 80 are excluded from participationXx_NEWLINE_xXHistory of hypersensitivity to docetaxel or polysorbate 80Xx_NEWLINE_xXPatients with prior docetaxel chemotherapyXx_NEWLINE_xXPatients must have received at least one of the approved products known to improve the overall survival of patients with metastatic castration resistant prostate cancer (i.e. abiraterone, enzalutamide, sipuleucel-t, radium-223, docetaxel or cabazitaxel)Xx_NEWLINE_xXPatient has prior hypersensitivity reaction or intolerance to docetaxel or other drugs formulated with polysorbate 80Xx_NEWLINE_xXHave completed neurotoxic chemotherapy, i.e. taxanes (paclitaxel, docetaxel) and platinum (carboplatin) at least 3 months prior to enrollmentXx_NEWLINE_xXPain appeared during or up to 12 weeks after treatment with oxaliplatin, paclitaxel, docetaxel or any combination of theseXx_NEWLINE_xXAll gastrointestinal malignancies where the patient received oxaliplatin for cancer treatment or breast malignancies where patients have received docetaxel or paclitaxel for cancer treatmentXx_NEWLINE_xXHave metastatic castration-resistant prostate cancer (prostate cancer progressing despite castrate levels of testosterone [< 50 ng/dL] using standard measures of progression defined by Prostate Cancer Working Group 2), are chemo-naive for metastatic castration-resistant prostate cancer (mCRPC); patients must have symptomatic disease or visceral metastases or otherwise be eligible for docetaxel treatment per investigator judgment (e.g. for progression on imaging or rapidly rising PSA despite 2nd line hormonal treatment);\r\n* Note: Six cycles of prior docetaxel are allowed in hormone-sensitive disease, per Eastern Cooperative Oncology Group (ECOG) 3805 data and have been off of docetaxel for at least 12 monthsXx_NEWLINE_xXThe patient’s previous chemotherapy treatment must have included a taxane (paclitaxel, nab-paclitaxel, or docetaxel) and considered the primary cause of the neuropathy by the medical teamXx_NEWLINE_xXChemotherapy regimen: Docetaxel/carboplatin. Antiemetic regimen: Palonosetron on Day 1 + dexamethasone on Days 1, 2, & 3.Xx_NEWLINE_xXThe patient’s previous chemotherapy treatment must have included a taxane (paclitaxel, nab-paclitaxel, or docetaxel) or platinum (cisplatin, oxaliplatin, or carboplatin) and considered the primary cause of the neuropathy by the medical teamXx_NEWLINE_xXUndergoing current therapy for organ confined or systemic disease; this does not preclude patients who had previously received upfront docetaxel in the hormone sensitive settingXx_NEWLINE_xXPrior docetaxel-based chemotherapy is permitted but not requiredXx_NEWLINE_xX