Integrated sensing and communication (ISAC) is a promising approach that utilizes a single waveform for both information transmission and target object acquisition. In this study, we focus on the challenges posed by inter-user and inter-ISAC-antenna interference, specifically the self-interference from ISAC transmit antennas to receive antennas. Further, the benefit of a multi-functional ISAC scheme is clarified by comparing it with single function-aware schemes: sensing- and communication-aware approaches. To address these issues, we investigate the application of a zero-forcing (ZF)-based beamforming and power allocation (PA) technique. A sum rate maximization problem with a target object sensing signal-to-noise (SNR) threshold is formulated and split into two subproblems for improved tractability. To tackle the first subproblem of precoder design, we develop a constraint-aware greedy algorithm that employs communication SNR ordering. Subsequently, we propose a feasibility test-based algorithm to solve the second subproblem of PA.Through an extensive performance evaluation, encompassing computational complexity, sum rate, and ISAC received SNR, we verify that relying solely on a single function-aware scheme is insufficient for accommodating ISAC's multifunctional capabilities. Additionally, we demonstrate that a naive switching strategy between two single function-aware schemes can result in inefficient communication performance. Considering both sensing and communication functions, we identify the need for an adaptive balance between sensing and communication capabilities in a multi-functional ISAC system. This can be achieved by dynamically adjusting the target object sensing SNR threshold within the optimization problem's constraint. The proposed ZF-based ISAC with the designed PA scheme offers an optimal strategy when the transmit power of the ISAC is low. Conversely, an equal PA to multiple users emerges as the best strategy when the transmit power of the ISAC is sufficiently high. In conclusion, our study highlights the significance of integrating sensing and communication functionalities in ISAC systems. Moreover, by providing insights into the interplay between target object sensing, beamforming, and power allocation, we contribute to the development of efficient and adaptable ISAC architectures.