Fourier Ptychography is a new computational microscopy technique that achieves gigapixel images with both wide field of view and high resolution in both phase and amplitude. The hardware setup involves a simple replacement of the microscope's illumination unit with a programmable LED array, allowing one to flexibly pattern illumination angles without any moving parts. In previous work, a series of low-resolution images was taken by sequentially turning on each single LED in the array, and the data were then combined to recover a bandwidth much higher than the one allowed by the original imaging system. Here, we demonstrate a multiplexed illumination strategy in which multiple randomly selected LEDs are turned on for each image. Since each LED corresponds to a different area of Fourier space, the total number of images can be significantly reduced, without sacrificing image quality. We demonstrate this method experimentally in a modified commercial microscope. Compared to sequential scanning, our multiplexed strategy achieves similar results with approximately an order of magnitude reduction in both acquisition time and data capture requirements.