End-to-end transformer-based trackers have achieved remarkable performance on most human-related datasets. However, training these trackers in heterogeneous scenarios poses significant challenges, including negative interference - where the model learns conflicting scene-specific parameters - and limited domain generalization, which often necessitates expensive fine-tuning to adapt the models to new domains. In response to these challenges, we introduce Parameter-efficient Scenario-specific Tracking Architecture (PASTA), a novel framework that combines Parameter-Efficient Fine-Tuning (PEFT) and Modular Deep Learning (MDL). Specifically, we define key scenario attributes (e.g, camera-viewpoint, lighting condition) and train specialized PEFT modules for each attribute. These expert modules are combined in parameter space, enabling systematic generalization to new domains without increasing inference time. Extensive experiments on MOTSynth, along with zero-shot evaluations on MOT17 and PersonPath22 demonstrate that a neural tracker built from carefully selected modules surpasses its monolithic counterpart. We release models and code.