As a key unit of future high-throughput communications, optical analog to digital converter (OADC) with all-optical quantizer element that simultaneously possesses high resolution, large bandwidth and compact size is highly promising. A pending issue of conventional OADC methods is that a higher resolution is always accompanied with dramatically increased system size and complexity, consequently magnified impact of system error on the performance index such as bandwidth, which fails the inherent superiority of OADC. In this paper, we propose and numerically investigate a cascaded optical quantization (COQ) solution aiming to address the wavelength sensitivity issue of integrable optical phase-shifted quantizers at high resolution (>= 5-bit). Harnessing a step-size multimode interference coupler and a shape-optimized power splitter, we predict the operation bandwidth for 1-bit degradation can be up to 20 nm, 15.8 nm and 11.9 nm for the quantization resolution of 5-, 6-and 7-bit respectively, indicating a bandwidth improvement of > 1 THz compared to those without COQ. Meanwhile, the total insertion loss can be maintained below -1 dB. This proposed quantizer is CMOS-compatible, which can be monolithically integrated on the silicon-on-insulator (SOI) platform and fabricated through a commercial Multi-Project Wafer (MPW) run. It paves the path to achieve high-resolution and large bandwidth OADC chips in a cost-effective way.