We present our submission to the unconstrained subtask of the SIGTYP 2024 Shared Task on Word Embedding Evaluation for Ancient and Historical Languages for morphological annotation, POS-tagging, lemmatization, character- and word-level gap-filling. We developed a simple, uniform, and computationally lightweight approach based on the adapters framework using parameter-efficient fine-tuning. We applied the same adapter-based approach uniformly to all tasks and 16 languages by fine-tuning stacked language- and task-specific adapters. Our submission obtained an overall second place out of three submissions, with the first place in word-level gap-filling. Our results show the feasibility of adapting language models pre-trained on modern languages to historical and ancient languages via adapter training.