In real-time systems, schedulability analyses provide the required timing guarantees. However, current suspension-aware analyses are limited to Task-Level Fixed-Priority (TFP) scheduling or Earliest-Deadline-First (EDF) scheduling of constrained-deadline self-suspending task systems. In this work, we provide a unifying schedulability analysis for uniprocessor Global EDF-Like (GEL) schedulers of arbitrary-deadline task sets. While analyses for EDF-Like schedulers are rare, many widely used scheduling algorithms can be considered as EDF-Like, for example, EDF, First-In-First-Out (FIFO), Earliest-Quasi-Deadline-First (EQDF), and Suspension-Aware EDF (SAEDF). Therefore, the provided analysis is applicable to those algorithms. Moreover, it can be applied to TFP scheduling as well. Our analysis is the first suspension-aware schedulability analysis for arbitrary-deadline sporadic real-time task systems under Job-Level Fixed-Priority (JFP) scheduling, such as EDF, and the first unifying suspension-aware schedulability analysis framework that covers a wide range of scheduling algorithms. Through numerical simulations, we show that our analysis improves the state of the art for constrained-deadline EDF scenarios.