Knowledge distillation (KD) involves training a small “student” model to replicate the strong performance of a high-capacity “teacher” model, enabling efficient deployment in resource-constrained settings. Top-performing methods tend to be task- or architecture-specific and lack generalizability. Several existing approaches require pretraining of the teacher on task-specific datasets, which can be costly for large and unstable for small datasets. Here we propose an approach for improving KD through a novel distillation loss agnostic to the task and model architecture. We successfully apply our method to the distillation of the BERT-base and achieve highly competitive results from the distilled student across a range of GLUE tasks, especially for tasks with smaller datasets.