Deploying natural language processing (NLP) models on mobile platforms requires models that can adapt across diverse applications while remaining efficient in memory and computation. We investigate pre-finetuning strategies to enhance the adaptability of lightweight BERT-like encoders for two fundamental NLP task families: named entity recognition (NER) and text classification. While pre-finetuning improves downstream performance for each task family individually, we find that naïve multi-task pre-finetuning introduces conflicting optimization signals that degrade overall performance. To address this, we propose a simple yet effective multi-task pre-finetuning framework based on task-primary LoRA modules, which enables a single shared encoder backbone with modular adapters. Our approach achieves performance comparable to individual pre-finetuning while meeting practical deployment constraint. Experiments on 21 downstream tasks show average improvements of +0.8% for NER and +8.8% for text classification, demonstrating the effectiveness of our method for versatile mobile NLP applications.