Ixabepilone in Treating Patients With Metastatic or Recurrent Squamous Cell Cancer of the Head and Neck

Inclusion Criteria: * Patients must have measurable histologically confirmed squamous cell carcinoma of the head and neck, excluding nasopharyngeal primaries, that is incurable with surgery or radiation therapy; disease must be measurable as defined by RECIST =\< 4 weeks of randomization * Patients must have distant metastases or locoregional recurrence or persistent disease within a radiation portal * Baseline tumor measurements/evaluations must be obtained \< 4 weeks prior to randomization * Patients may have received up to one prior biotherapy regimen and treatment must have been completed at least 4 weeks prior to randomization; no more than two prior chemotherapy regimens for recurrent and/or metastatic disease are permitted; patients may have received prior docetaxel or paclitaxel, but must not have been previously treated with an investigational taxane; chemotherapy treatment must have been completed at least 4 weeks prior to randomization * If the only site of measurable disease is a previously irradiated area, the patient must have documented progressive disease or biopsy-proven residual carcinoma; persistent disease after radiotherapy must be biopsy-proven at least 8 weeks after the completion of radiotherapy; patients must have completed radiotherapy at least 4 weeks prior to randomization * Patients must not have a concurrent malignancy except curatively treated basal or squamous cell carcinoma of the skin or carcinoma in situ of the cervix; patients with prior malignancies who have been disease-free \> 2 years are eligible * Patients must have ECOG performance status of 0 or 1 * Absolute neutrophil count (ANC) \>= 1500/mm\^3 * Platelet count \>= 100,000/mm\^3 * Serum creatinine =\< 1.2 mg OR creatinine clearance \>= 50 ml/min NOTE: Either calculated or actual creatinine clearance can be used NOTE: The creatinine clearance may be calculated by the Cockcroft-Gault formula * Total bilirubin =\< 1.5 mg * (SGOT) AST, (SGPT) ALT =\< 2 x institutional upper limit of normal * Alkaline phosphatase =\< 2 x institutional upper limit of normal * Serum calcium within institutional normal range and no history of malignancy associated hypercalcemia * Patients must not have a pre-existing peripheral neuropathy \>= grade 2 * Patients must not have an active infection nor currently be receiving treatment for a recent infection * Patients must have recovered from the effects of any recent surgery * Female patients must not be pregnant or breastfeeding; the effects of BMS-247550 on pregnant women and on fetuses are unknown; however, the known toxicities, which include neutropenia, are likely to place pregnant women at increased risk; the mechanism of action of this compound, stabilization of microtubules in dividing cells, is highly likely to be teratogenic; taxanes, which have a similar mechanism of action, are known to be teratogenic NOTE: A negative serum pregnancy test is required =\< 2 weeks of randomization for women of childbearing potential * Women of childbearing potential and sexually active males must agree to use an accepted and effective method of contraception * Patients must not have a known hypersensitivity to castor oil, or agents containing Cremophor El, or paclitaxel; patients with a history of grade 1 or uncomplicated, non-recurrent grade 2 hypersensitivity reactions associated with Cremophor will be eligible with prophylaxis