Prior treatment with docetaxel within months of study enrollment taxanes (paclitaxel or docetaxel) or epirubicin, Docetaxel monotherapy is a reasonable treatment in the judgement of the Investigator Prior use of abiraterone acetate, enzalutamide, docetaxel, cabazitaxel, carboplatin, or radium- for the treatment of castration-resistant disease\r\n* Prior docetaxel use in the hormone-sensitive disease setting is allowed, but must be completed >= weeks prior to enrollment\r\n* Prior sipuleucel-T use is allowed, but must be completed >= weeks prior to enrollment\r\n* Concurrent use of zolendronic acid or denosumab is allowed on study Prior systemic chemotherapy (docetaxel, cabazitaxel, estramustine, other cytotoxic agents) Prior 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 > months prior to study registration Agree to use barrier methods of birth control during the docetaxel portion of the protocol and for at least one month after last docetaxel administration Any previous exposure to docetaxel Patients planned to receive docetaxel with contra-indications to receive docetaxel Has known grade >= docetaxel-related toxicities or docetaxel toxicity related dose interruption or discontinuation Prior chemotherapy (e.g. docetaxel, cabazitaxel) for CRPC; prior docetaxel administered in the castrate-sensitive space is allowed Prior treatment with ADI-PEG , gemcitabine, or docetaxel Prior systemic chemotherapy (docetaxel, cabazitaxel, estramustine, other cytotoxic agents) Prior 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 v. and PCWG\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 v. and PCWG Docetaxel 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 therapy Has had any previous exposure to paclitaxel or docetaxel in the last years. Radiographic progressive disease, irrespective of PSA changes, after receiving at least cycles of docetaxel or cabazitaxel Docetaxel: Creatinine clearance no minimum Received more than cycles of docetaxel (for docetaxel cohort only) or of cabazitaxel (for cabazitaxel cohort only) Last docetaxel or cabazitaxel dose > weeks prior to enrollment Progressive disease, both docetaxel naive and docetaxel treated. Less than weeks since last myelosuppressive therapy (including Docetaxel, Cabazitaxel, Ra, Sm) or other radionuclide therapy. A minimum of weeks from prior chemotherapy, including but not limited to, docetaxel, cabazitaxel, mitoxantrone, carboplatin, cisplatin, or estramustine; if applicable, prior to registration Previous treatment with docetaxel or an Axl inhibitor Received any prior treatment with any taxane (docetaxel or paclitaxel) for small cell lung cancer Prior adjuvant chemotherapy with gemcitabine and/or docetaxel/paclitaxel is allowed Prior 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- Prior cytotoxic chemotherapy (for example, but not limited to, docetaxel, mitoxantrone, cabazitaxel) within months of registration is prohibited ARM B COHORT : Patients must not have prior exposure to docetaxel ARM B COHORT : Patients must not have prior exposure to docetaxel Prior treatments with Cyp inhibitors like TAK-/orteronel, ketoconazole, radium or docetaxel (up to cycles of docetaxel given in the non CRPC setting is allowed); prior treatment with sipuleucel-T is allowed Patients who have had prior therapy with gemcitabine or docetaxel Prior therapy with docetaxel Patients previously treated with docetaxel for NSCLC or with known severe hypersensitivity to taxane therapies. Prior therapy with a MEK-inhibitor or docetaxel for metastatic non-small cell lung cancer (docetaxel in the adjuvant setting will be allowed) No 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] > months ago will be eligible); prior abiraterone is allowed Prior treatment with docetaxel or cabazitaxel for mCRPC Prior treatment with docetaxel. Patients must have progressed on Arm (docetaxel) of this sub-study Patients must have progressed on Arm (docetaxel) of this sub-study Patients must have progressed on Arm (docetaxel) of this sub-study Prior treatment with docetaxel is allowed but not required Up to cycles of docetaxel therapy with final treatment administration completed within months of day and no evidence of disease progression during or after the completion of docetaxel therapy; Participants who received docetaxel treatment must meet the following criteria: a) Received a maximum of cycles of docetaxel therapy for mHSPC; b) Received the last dose of docetaxel <= months prior to randomization; c) Maintained a response to docetaxel of stable disease or better, by investigator assessment of imaging and PSA, prior to randomization Taking any other systemic anticancer agent (docetaxel, doxorubicin, irinotecan) Have not received prior treatment with docetaxel. Patients who have disease progression during, or after, receiving docetaxel and have had at least 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. Prior therapy with docetaxel for NSCLC Prior treatment with any of the chemotherapy medications (cisplatin or docetaxel) for HNSCC or with AZD Prior cytotoxic chemotherapy with the exception of docetaxel or cabazitaxel; treatment with docetaxel or cabazitaxel must be discontinued >= weeks from the time of enrollment, and recovery of adverse events (AEs) to grade or baseline (however, ongoing neuropathy is permitted) Patients must have one of the following a) low volume disease (defined as no visceral metastases and < bone metastases) or b) are not candidates for docetaxel based chemotherapy or c) refused docetaxel chemotherapy Prior treatment with eribulin, fulvestrant or anastrozole, paclitaxel, abraxane, docetaxel, vinorelbine, or capecitabine For 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 cycles of chemotherapy. Prior disease progression on docetaxel or paclitaxel in metastatic setting Prior cytotoxic chemotherapy (e.g. docetaxel, mitoxantrone, cabazitaxel) within months of registration is prohibited Prior treatment with Docetaxel Prior 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 # and did not experience significant drug related toxicity Planned 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 days before enrollment (late enrollers) Known hypersensitivity to docetaxel, fluorouracil (-FU) Patients who have received previous docetaxel or cisplatin Prior treatment with docetaxel-based chemotherapy Prior treatment with docetaxel within months of enrollment Previous treatment with docetaxel. Hypersensitivity to the active substance or ingredients of PEGPH and docetaxel. Received prior treatment with docetaxel. Patients receiving chemotherapy (e.g., docetaxel, cabazitaxel, taxane, or platinum as single agents or in combination) as their cancer treatment Patient must be eligible for chemotherapy with docetaxel Prior treatment with trastuzumab emtansine, docetaxel, or paclitaxel either as single\n agents or as part of a treatment regimen. Symptomatic patients who, in the opinion of the investigator, may benefit from docetaxel-based chemotherapy Prior treatment with docetaxel or mogamulizumab; Prior treatment with docetaxel Prior treatment with MLN; however, prior treatment with docetaxel, paclitaxel, and carboplatin is allowed. Prior treatment with docetaxel for recurrent or advanced NSCLC Prior treatment with docetaxel-containing therapy Prior treatment with MLN; however, prior treatment with docetaxel, paclitaxel,carboplatin, and gemcitabine is allowed Participants 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 treatment Received prior docetaxel chemotherapy Part only: Patients must be docetaxel-naive. Part only: Patients may not have had prior treatment with docetaxel. History of treatment with docetaxel in any setting. Participants treated with prior paclitaxel are eligible. Prior treatment with docetaxel-based chemotherapy Patients with prior docetaxel chemotherapy Pain appeared during or up to weeks after treatment with oxaliplatin, paclitaxel, docetaxel or any combination of these Undergoing current therapy for organ confined or systemic disease; this does not preclude patients who had previously received upfront docetaxel in the hormone sensitive setting Prior docetaxel-based chemotherapy is permitted but not required