Cabazitaxel With or Without Carboplatin in Treating Patients With Previously Treated Metastatic Castration-Resistant Prostate Cancer

Inclusion Criteria: * Histologic evidence of prostate adenocarcinoma * In addition to patients with adenocarcinoma, patients with "anaplastic" features are also eligible as defined by at least one of the following: a) histologic evidence of small cell prostate cancer (patients with small cell carcinoma on histology are not required to demonstrate castration-resistant progression); b) any of the following metastatic presentations: (i) exclusive visceral metastases; (ii) radiographically predominant lytic bone metastases identified by plain X-ray or computed tomography (CT) scan; (iii) bulky (\>= 5 cm in longest dimension) lymphadenopathy (iv) bulky (\>= 5 cm) tumor mass in the prostate/pelvis (v) low PSA (=\< 10 ng/ml) at initial presentation (prior to androgen ablation or at symptomatic progression in the castrate-setting) plus high volume (\>= 20) bone metastases; (vi) elevated serum lactate dehydrogenase (LDH) (\>= 2 x ULN) or elevated serum carcinoembryonic antigen (CEA) (\>= 2 x upper limit of normal \[ULN\]) in the absence of other etiologies; (vii) short interval (=\< 180 days) to castrate-resistant progression following initiation of hormonal therapy * Castration-resistant prostate cancer; patients must have surgical or ongoing chemical castration (with luteinizing-hormone-releasing hormone \[LHRH\] agonists or LHRH antagonists), with a baseline testosterone level \< 50 ng/dL * Metastatic disease; patients must have evidence for metastatic prostate cancer by bone scan…