The rapid evolution of error-resilient programs intertwined with their quest for high throughput has motivated the use of Single Instruction, Multiple Data (SIMD) components in Field-Programmable Gate Arrays (FPGAs). Particularly, to exploit the error-resiliency of such applications, Cross-layer approximation paradigm has recently gained traction, the ultimate goal of which is to efficiently exploit approximation potentials across layers of abstraction. From circuit- to application-level, valuable studies have proposed various approximation techniques, albeit linked to four drawbacks: First, most of approximate multipliers and dividers operate only in SISD mode. Second, imprecise units are often substituted, merely in a single kernel of a multi-kernel application, with an end-to-end analysis in Quality of Results (QoR) and not in the gained performance. Third, state-of-the-art (SoA) strategies neglect the fact that each kernel contributes differently to the end-to-end QoR and performance metrics. Therefore, they lack in adopting a generic methodology for adjusting the approximation knobs to maximize performance gains for a user-defined quality constraint. Finally, multi-level techniques lack in being efficiently supported, from application-, to architecture-, to circuit-level, in a cohesive cross-layer hierarchy.In this article, we propose Plasticine, a cross-layer methodology for multi-kernel applications, which addresses the aforementioned challenges by efficiently utilizing the synergistic effects of a chain of techniques across layers of abstraction. To this end, we propose an application sensitivity analysis and a heuristic that tailor the precision at constituent kernels of the application by finding the most tolerable degree of approximations for each of consecutive kernels, while also satisfying the ultimate user-defined QoR. The chain of approximations is also effectively enabled in a cross-layer hierarchy, from application- to architecture- to circuit-level, through the plasticity of SIMD multiplier-dividers, each supporting dynamic precision variability along with hybrid functionality. The end-to-end evaluations of Plasticine on three multi-kernel applications employed in bio-signal processing, image processing, and moving object tracking for Unmanned Air Vehicles (UAV) demonstrate 41%-64%, 39%-62%, and 70%-86% improvements in area, latency, and Area-Delay-Product (ADP), respectively, over 32-bit fixed precision, with negligible loss in QoR. To springboard future research in reconfigurable and approximate computing communities, our implementations will be available and open-sourced at https://cfaed.tu-dresden.de/pd-downloads.