This work presents a dynamic characterization of a multi-level Chireix outphasing (ML-CO) power amplifier (PA) with modulated signals. The ML-CO technique combines the advantages of envelope tracking and outphasing architectures by limiting the supply modulation to discrete levels with an efficient power-DAC modulator and using outphasing for fine amplitude control. We describe an experimental test bench that supplies the required phase-and time-aligned modulated signals for outphasing and supply modulation simultaneously. Pulsed characterization is used to design a multi-level memory-less polynomial DPD. The linearized ML-CO GaN X-band MMIC PA is demonstrated with fixed input drive levels for 9.3-dB PAPR, 1.4-MHz and 11.3-dB PAPR, 10-MHz LTE signals with a 9.7 GHz carrier. For both signals, the average total power consumption is reduced by a factor of two when supply modulation is used. An investigation of control signal generation strategies is presented, including combinations of discrete supply and continuous input modulation. A simple exponential function tracks the optimal efficiency trajectory of the ML-CO PA, enabling overall efficiency improvements within 9 and 27 percentage points. This control strategy is applied to radar pulses with amplitude shaping and frequency chirp, with efficiency improvement of up to 11.8 percentage points compared to constant-supply operation, with 29 dB improvement in spectral confinement.