BootCMatchGX is a high-performance numerical library under development for the solution of extremely large sparse linear systems on modern heterogeneous HPC platforms. The library is designed to exploit the computational throughput and energy efficiency of GPU accelerators, targeting problems whose size and memory footprint exceed the capacity of a single compute node. Recently, BootCMatchGX has been extended with a bootstrap-based algebraic multilevel framework that automatically constructs and combines multiple AMG hierarchies. The bootstrap process generates a sequence of AMG components, each specifically tailored to capture different algebraically smooth error components. These hierarchies are then combined—typically in a multiplicative or symmetrized fashion—into a composite solver that achieves a prescribed convergence rate while keeping the operator complexity under control. The bootstrap formulation provides strong robustness with respect to coefficient heterogeneity and discretization effects, and it is particularly effective for problems characterized by a multi-dimensional near kernel. Unlike traditional AMG approaches that require explicit a priori information, BootCMatchGX naturally handles systems arising from linear elasticity, where multiple rigid body modes define a multi-vector near kernel that often degrades the performance of standard solvers. From a performance perspective, BootCMatchGX adopts GPU-oriented design strategies aimed at minimizing data movement, maximizing concurrency, and overlapping communication with computation. The library supports multi-GPU execution and targets large-scale heterogeneous systems, with performance results complemented by energy measurements that highlight the sustainability of the proposed approach.