Owing to the diverse geographical distributions of users, multi-layered satellite networks tend to exhibit high variances causing traffic concentrations at particular satellites to increase drastically. This results in high packet drop rates and severe degradation of Quality of Service (QoS). The Explicit Load Balancing (ELB) scheme was developed to address these issues in Low Earth Orbit (LEO) satellite networks by having the satellites, which experience heavy traffic, redirect a portion of the traffic via alternative paths. To cope with network congestion (over a single layer) and for better traffic distribution, multi layer satellites were proposed. In this paper, we propose an efficient traffic distribution scheme for multilayered satellite networks based on ELB in which we extend the range for exchanging the traffic-load information for achieving further reductions in packet drop rates. We also present an enhanced technique for efficiently computing the detouring ratio. The effectiveness of the envisioned approach is validated via simulations.