It is understood that in a network with an in-band full-duplex (FD) access point (AP) simultaneously serving multiple half-duplex clients, various kinds of interference may severely degrade the network spectral efficiency (SE). In this paper, we first address the problem of canceling the interclient interference (ICI) from multiple uplink clients to multiple downlink clients in such a scenario. The proposed ICI nulling approach, namely, multiuser ICI cancellation (MU-IC2), enables the AP to actively and completely eliminate the ICI for the downlink clients. With this method, the gain from FD processing can be achieved much efficiently. Design guideline is given and reduced-complexity implementation for use with a large number of antennas at the AP is also derived. Furthermore, in some circumstances, notable residual self-interference (SI) exists at the AP due to the imperfection of SI cancellation during the FD operation. This may enlarge the interference observed by the downlink clients. We provide new ways, i.e., two MU-SI-IC2 approaches, to deal with this case based on the possible knowledge of SI as well. As a result, both the SI-induced interference and ICI are effectively eliminated, and the overall throughput can still be benefited from FD and kept at a high level. The simulation results show that in terms of the network SE, our proposed MU-IC2 and MU-SI-IC2 can significantly outperform some baseline schemes and the state-of-the-art active ICI mitigation methods in various scenarios.