Symbol-level precoding is a new paradigm for multiuser multiple-antenna downlink systems aimed at creating constructive interference among transmitted data streams. This can be enabled by designing the precoded signal of the multiantenna transmitter on a symbol level, taking into account both channel state information and data symbols. Previous literature has studied this paradigm for Mary phase shift keying modulations by addressing various performance metrics, such as power minimization and maximization of the minimum rate. In this paper, we extend this to generic multi-level modulations, i.e., Mary quadrature amplitude modulation by establishing connection to PHY layer multicasting with phase constraints. Furthermore, we address the adaptive modulation schemes which are crucial in enabling the throughput scaling of symbol-level precoded systems. In this direction, we design the signal processing algorithms for minimizing the required power under per-user signal to interference noise ratio or goodput constraints. Extensive numerical results show that the proposed algorithm provides considerable power and energy efficiency gains, while adapting the employed modulation scheme to match the requested data rate.