Most classroom tutors powered by large language models default to answer-giving rather than cultivating reasoning; this research presents an alternative: a supervised, multi-agent tutoring architecture that makes students explain, justify, and revise their ideas while the system enforces milestone-aligned progress. A peer-like Socratic agent conducts grade-appropriate exchanges; a supervisory loop checks alignment with instructional goals and prevents answer leakage; an evaluation layer tracks reasoning quality; and a retrieval component offers grounded hints while strictly separating external knowledge from what the student has taught the agent. Teachers pre-upload lesson artifacts, which are ingested into an Available Knowledge Memory to gate hints, ground evaluations, and anchor milestone checks to curriculum-specific evidence. An 8-week feasibility study across grades 5–10 (10 teachers, 627 students) used a baseline and three post-assessments (scores normalized to 0–1), plus teacher diaries and focus groups. A linear mixed-effects analysis showed a significant positive effect of time (p = .03), with heterogeneous gains across classrooms. The central contribution is a multi-agent AI tutoring system to elevate students’ reasoning and thinking; its educational significance lies in making formative feedback more scalable, aligning guidance with curriculum goals, and offering a practical path to classroom-ready deployment of AI tutors.