Recent Large Reasoning Models (LRMs) achieve strong performance by leveraging long-form Chain-of-Thought (CoT) reasoning, but uniformly applying overlong reasoning at inference time incurs substantial and often unnecessary computational cost. To address this, prior work explores various strategies to infer an appropriate reasoning budget from the input. However, such approaches are unreliable in the worst case, as estimating the minimal required reasoning effort is fundamentally difficult, and they implicitly fix the trade-off between reasoning cost and accuracy during training, limiting flexibility under varying deployment scenarios. Motivated by these limitations, we propose ORBIT, a controllable multi-budget reasoning framework with well-separated reasoning modes triggered by input. ORBIT employs multi-stage reinforcement learning to discover Pareto-optimal reasoning behaviors at each effort, followed by on-policy distillation to fuse these behaviors into a single unified model. Experiments show that ORBIT achieves (1) controllable reasoning behavior over multiple modes, (2) competitive reasoning density within each mode, and (3) integration of these frontier policies into a single unified student model while preserving clear mode separation and high per-mode performance.