Event logs record enterprise service processes as sequences of timestamped activities. Predictive process monitoring typically trains a separate model per event log, requiring retraining when processes, activity vocabularies, or time scales change.We study an event-log-native foundation model pretrained once on heterogeneous logs and adapted to an unseen log with a small labeled support set, without fitting a separate model for that log. The model represents prefixes with a mixture-of-experts transformer and predicts next activity and remaining time with a support-conditioned prototypical head whose label space is defined by the support context.To align training with deployment, we incorporate retrieval-centric objectives that shape the representation for nearest-neighbor support selection and we provide confidence estimates for both classification and regression.We benchmark this no-fine-tuning setting on five public logs against classical CPU-friendly baselines and a general-purpose in-context tabular predictor, down to 0.5% of training cases. Results show that one pretrained predictor can be competitive, but performance depends on retrieving suitable supports; in several settings, simple kNN on learned embeddings matches the full head.We also find that activity-time dependence is informative in this benchmark, and that confidence scores support useful performance stratification and expert-level representation analysis.