Adapters are an efficient, composable alternative to full fine-tuning of pre-trained models and help scale the deployment of large ASR models to many tasks. In practice, a task ID is commonly prepended to the input during inference to route to single-task adapters for the specified task. However, one major limitation of this approach is that the task ID may not be known during inference, rendering it unsuitable for most multi-task settings. To address this, we propose three novel task-ID-free methods to combine single-task adapters in multi-task ASR and investigate two learning algorithms for training. We evaluate our methods on 10 test sets from 4 diverse ASR tasks and show that our methods are non-destructive and parameter-efficient. While only updating 17% of the model parameters, our methods can achieve an 8% mean WER improvement relative to full fine-tuning and are on-par with task-ID adapter routing.