Genomic sequence alignment is an important research topic in bioinformatics and continues to attract significant efforts. As genomic data grow exponentially, however, most of alignment methods face challenges due to their huge computational costs. HMMER, a suite of bioinformatics tools, is widely used for the analysis of homologous protein and nucleotide sequences with high sensitivity, based on profile hidden Markov models (HMMs). Its latest version, HMMER3, introdues a heuristic pipeline to accelerate the alignment process, which is carried out on central processing units (CPUs) with the support of streaming SIMD extensions (SSE) instructions. Few acceleration results have since been reported based on HMMER3. In this paper, we propose a five-tiered parallel framework, CUDAMPF++, to accelerate the most computationally intensive stages of HMMER3's pipeline, multiple/single segment Viterbi (MSV/SSV), on a single graphics processing unit (GPU). As an architecture-aware design, the proposed framework aims to fully utilize hardware resources via exploiting finer-grained parallelism (multi-sequence alignment) compared with its predecessor (CUDAMPF). In addition, we propose a novel method that proactively sacrifices L1 Cache Hit Ratio (CHR) to get improved performance and scalability in return. A comprehensive evaluation shows that the proposed framework outperfroms all existig work and exhibits good consistency in performance regardless of the variation of query models or protein sequence datasets. For MSV (SSV) kernels, the peak performance of the CUDAMPF++ is 283.9 (471.7) GCUPS on a single K40 GPU, and impressive speedups ranging from 1.x (1.7x) to 168.3x (160.7x) are achieved over the CPU-based implementation (16 cores, 32 threads).