Arclike bunch compressors are important components in recirculating accelerator linacs, energy recovery linacs, and high-brightness light sources. However, their design is complicated by longitudinal nonlinear optics and coherent synchrotron radiation (CSR), including both steady-state CSR (ss CSR) in bending magnets and CSR in the subsequent drifts (dr CSR). These effects can degrade the longitudinal compression quality, generate current spikes, and induce transverse emittance growth. In this work, we develop an analytical framework for evaluating CSR effects in complex arclike compressors without relying on the small-angle approximation. The proposed method includes both ss and dr CSR contributions and is applied to the mitigation of CSR-induced transverse displacements as well as to longitudinal matching with nonlinear compression. Based on these methods, a two-stage arclike compressor using an asymmetric quadruple-bend-achromat structure is designed. Numerical simulations show that the proposed compressor can compress a (100~) bunch to nearly (50~) while maintaining negligible emittance growth. The analytical model is further used to study CSR-induced modifications to the compression process, including rms bunch length and peak-current behavior. Benchmarking against Bmad simulations demonstrates good agreement, confirming the model as an efficient tool for compressor design and optimization.