We present the multiple particle identification (MPID) network, a convolutional neural network (CNN) for multiple object classification, developed by MicroBooNE. MPID provides the probabilities of $e^-$, $\gamma$, $\mu^-$, $\pi^\pm$, and protons in a single liquid argon time projection chamber (LArTPC) readout plane. The network extends the single particle identification network previously developed by MicroBooNE. MPID takes as input an image either cropped around a reconstructed interaction vertex or containing only activity connected to a reconstructed vertex, therefore relieving the tool from inefficiencies in vertex finding and particle clustering. The network serves as an important component in MicroBooNE's deep learning based $\nu_e$ search analysis. In this paper, we present the network's design, training, and performance on simulation and data from the MicroBooNE detector.