Fixed-priority scheduling with deferred preemption(FPDS) and fixed-priority scheduling with preemption thresholds(FPTS) have been proposed in the literature as viable alternatives to fixed-priority preemptive scheduling (FPPS), that reduce memory requirements, reduce the cost of arbitrary preemptions, and may improve the feasibility of a task set even when preemption overheads are neglected. This paper aims at advancing the relative strength of limited preemptive schedulers by combining FPDS and FPTS. In particular, we present a refinement of FPDS with preemption thresholds for both jobs and sub-jobs, termed FPGS. We provide an exact schedulability analysis for FPGS, and show how to maximize the feasibility of a set of sporadic tasks under FPGS for given priorities, computation times, periods, and deadlines of tasks. We evaluate the effectiveness of FPGS by comparing the feasibility of task sets under FPGS with other fixed-priority scheduling algorithms by means of a simulation. Our experiments show that FPGS allows an increase of the number of task sets that are schedulable under fixed-priority scheduling.