Trastuzumab and Docetaxel in Treating Patients Who Have Metastatic Prostate Cancer That Is Refractory to Hormone Therapy

DISEASE CHARACTERISTICS: Histologically confirmed stage IV prostate cancer (any T, any N, M1, any G; D3) Clinical evidence of metastatic disease in bone or soft tissue Her2/neu-positive (2+ and 3+) by immunochemistry or fluorescent in situ hybridization Androgen-independent Serum PSA at least 10 ng/mL that has risen on 3 successive evaluations after prior hormonal therapy At least 1 month since prior antiandrogen therapy (e.g., flutamide, bicalutamide, or nilutamide) and rising PSA levels with 1 of the 2 rising PSA levels, measured at least 2 weeks apart, after antiandrogen withdrawal Bone only disease and elevated PSA alone allowed LHRH analog therapy must continue in patients who have not had prior orchiectomy and have castrate levels of testosterone PATIENT CHARACTERISTICS: Age: 18 and over Performance status: SWOG 0-2 Life expectancy: At least 12 weeks Hematopoietic: WBC at least 3,500/mm3 Absolute granulocyte count at least 1,800/mm3 Platelet count at least lower limit of normal (LLN) Hepatic: Bilirubin no greater than 2 times upper limit of normal (ULN) SGOT no greater than 2 times ULN Renal: Creatinine no greater than 1.6 mg/dL Creatinine clearance at least 50 mL/min Cardiovascular: Ejection fraction more than 50% or more than LLN by MUGA scan or 2-D echocardiogram No symptomatic coronary artery disease No active ischemia on EKG Other: Fertile patients must use effective contraception No other prior malignancy within the past 5 years except adequately treated basal cell or squamous cell skin cancer PRIOR CONCURRENT THERAPY: Biologic therapy: No concurrent biologic therapy Chemotherapy: No more than one prior nonanthracycline chemotherapy regimen (including suramin) Endocrine therapy: See Disease Characteristics No concurrent corticosteroids as antiemetic Radiotherapy: At least 4 weeks since prior radiotherapy At least 3 months since prior strontium chloride Sr 89 and recovered No concurrent radiotherapy to measurable lesions Surgery: See Disease Characteristics