This work presents throughput-enhanced readout ASIC (TERA), an integrated multichannel analog pulse processor (APP), suitable for processing signals generated from solid-state detectors, such as silicon drift detectors (SDDs) coupled to pulsed reset-type charge-sensitive amplifiers (CSAs). In particular, this development targets applications at high count rates (≈Mcps) in energy-dispersive X-ray spectroscopy. The demonstrator chip is composed of four parallel readout channels. Each channel includes a seventh-order semi-Gaussian shaping amplifier with controllable shaping times and full-scale ranges, followed by a peak stretcher and switched-capacitor analog memory. Each channel is also equipped with a dedicated peak detector and a novel pile-up rejection (PUR) logic. Each pair of channels can be optionally digitized by a 12-bit on-chip successive-approximation-register (SAR) analog-to-digital converter (ADC), providing a digital output at a maximum sampling rate of 2.5 Msps. The architecture achieves high throughput and satisfactory energy resolution. In fact, in 55Fe spectroscopy measurements, when using the shortest shaping pulsewidth of 200 ns, a full-width at half-maximum (FWHM) Mn $\text{K}\alpha $ line of 159.4 eV (12.5 $\text{e}^{-}_{\text {rms}}$ ) was obtained at low rates (10 kcps). This energy resolution can be achieved, thanks to the minimization of the effect of the ballistic deficit, achieved by optimizing the SDD detector in terms of optimum biasing, low operating temperature (−37 °C), and small size (1-mm diameter). At 1.61 Mcps/channel input rate, an output count rate of 1.09 Mcps/channel and a resolution of 205.1 eV (19.7 $\text{e}^{-}_{\text {rms}}$ ) were achieved with a 4-mm-diameter SDD and optimum PUR settings. Simultaneous multichannel acquisition has been successfully performed. Such high-rate performances are, to our knowledge, the best ones reported so far for an APP, based on a spectroscopy-grade application-specific integrated circuit (ASIC), and very close to those achievable by a standard digital pulse processor (DPP). Therefore, TERA can represent an attractive, compact, and scalable pulse processing solution for high-rate multichannel energy-dispersive X-ray detection systems.