Convolutional Neural Networks (CNNs) are computationally intensive algorithms that currently require dedicated hardware to be executed. In the case of FPGA-Based accelerators, we point-out in this work the challenge of Multi-Operand Adders (MOAs) and their high resource utilization in an FPGA implementation of a CNN. To address this challenge, two optimization strategies, that rely on time-multiplexing and approximate computing, are investigated. At first glance, the two strategies looked promising to reduce the footprint of a given architectural mapping, but when synthesized on the device, none of them gave the expected results. Experimental sections analyze the reasons of these unexpected results.