In many speech recording applications, the recorded desired speech is corrupted by both noise and acoustic echo, such that combined noise reduction (NR) and acoustic echo cancellation (AEC) is called for. A common cascaded design corresponds to NR filters preceding AEC filters. These NR filters aim at reducing the near-end room noise (and possibly partially the echo) and operate on the microphones only, consequently requiring the AEC filters to model both the echo paths and the NR filters. In this paper, however, we propose a design with extended NR (NRext) filters preceding AEC filters under the assumption of the echo paths being additive maps, thus preserving the addition operation. Here, the NRext filters aim at reducing both the near-end room noise and the far-end room noise component in the echo, and operate on both the microphones and loudspeakers. We show that the succeeding AEC filters remarkably become independent of the NRext filters, such that the AEC filters are only required to model the echo paths, improving the AEC performance. Further, the degrees of freedom in the NRext filters scale with the number of loudspeakers, which is not the case for the NR filters, resulting in an improved NR performance.