Fully differential amplifiers require the use of common-mode feedback (CMFB) circuits to properly set the amplifiers operating point. Due to scaling trends in CMOS technology, modern amplifiers increasingly rely on cascading more than two stages to achieve sufficient gain. With multiple gain stages, different topologies for implementing CMFB are possible, whether using a single CMFB loop or multiple ones. However, the impact on performance of each CMFB approach has seldom been studied in the literature. The aim of this work is to guide the choice of the CMFB implementation topology evaluating performance in terms of stability, linearity, noise and common-mode rejection. We present a detailed theoretical analysis, comparing the relative performance of two CMFB configurations for 3-stage OTA topologies in an implementation-agnostic manner. Our analysis is then corroborated through a case study with full simulation results comparing the two topologies at the transistor level and confirming the theoretical intuition. An active-RC filter is used as an example of a high-linearity OTA application, highlighting a 6 dB improvement in P1dB in the multi-loop implementation with respect to the single-loop case.