Recent advances in large language models (LLMs) have enabled deep research systems that synthesize comprehensive, report-style answers to open-ended queries by combining retrieval, reasoning, and generation. Yet most frameworks rely on rigid workflows with one-shot scoping and long autonomous runs, offering little room for course correction if user intent shifts mid-process. We present SteER, a framework for Steerable deEp Research that introduces interpretable, mid-process control into long-horizon research workflows. At each decision point, SteER uses a cost-benefit formulation to determine whether to pause for user input or to proceed autonomously. It combines diversity-aware planning with utility signals that reward alignment, novelty, and coverage, and maintains a live persona model that evolves throughout the session. SteER outperforms state-of-the-art open-source and proprietary baselines by up to 22.80\% on alignment, leads on quality metrics such as breadth and balance, and is preferred by human readers in 85\%+ of pairwise alignment judgments. We also introduce a persona-query benchmark and data-generation pipeline. To our knowledge, this is the first work to advance deep research with an interactive, interpretable control paradigm, paving the way for controllable, user-aligned agents in long-form tasks.