It is conceivable that early generations of patterned media will utilize read heads whose dimensions are several times larger than an "island" of magnetization. For such a scenario, we propose a "multiple islands per read head" model where the output from the read head is a function of the magnetization from several independently written tracks of islands. In particular, we focus on a "3 islands per read head" model where the output from the read head is a function of the magnetization from three independently written tracks of islands. The readback signal is determined from a finite track-width magnetoresistive (MR) head model using reciprocity calculations, and two noise sources - island position jitter and AWGN electronics noise - are considered. By sampling the noisy signal at intervals corresponding to the down-track island separation, we obtain a discrete-time readback channel model whose performance is obtained under maximum-likelihood sequence detection.