Acceptance sampling plans are statistical quality control methods commonly used to efficiently verify product quality under controlled risks. Recent research has developed the multiple dependent-state sampling plan (MDSP), which incorporates historical lot quality information, and the repetitive group sampling plan (RGSP), which allows for repeat sampling, to enhance the cost-effectiveness of sampling inspections. The modified RGSP (MRGSP) integrates the sampling mechanisms of both MDSP and RGSP. However, investigative analyses have uncovered significant deficiencies in the sampling mechanisms of MDSP and RGSP, with potential problems in MRGSP being even more severe. Therefore, this paper proposes an adjustable MRGSP (AMRGSP) based on unilateral process capability indices to establish a more adaptive and flexible sampling mechanism, reducing the limitations of MRGSP. We derive the operational characteristic function and average sample number function of AMRGSP, and establish a nonlinear optimization model considering Type I and II errors to determine the optimal plan design. Performance comparisons of the proposed AMRGSP with recent sampling plans revealed that the proposed plan offers reliable lot discriminative power and significantly reduces the sample size required for inspection, providing excellent cost-effectiveness. Finally, we evaluate the proposed plan using a practical case study to demonstrate its applicability in practice.