Let H 1 , . . . , H k be graphs. The multicolor Ramsey number r(H 1 , . . . , H k ) is the minimum integer r such that in every edge-coloring of K r by k colors, there is a monochromatic copy of H i in color i for some 1 ≤ i ≤ k. In this paper, we investigate the multicolor Ramsey number r(K 2,t , . . . , K 2,t , K m ), determining the asymptotic behavior up to a polylogarithmic factor for almost all ranges of t and m. Several different constructions are used for the lower bounds, including the random graph and explicit graphs built from finite fields. A technique of Alon and Rödl using the probabilistic method and spectral arguments is employed to supply tight lower bounds. A sample result isfor any t and m, where c 1 and c 2 are absolute constants.