Generating several solutions can expose alternative methods, but additional trajectories often paraphrase one dominant approach. We investigate whether the conditional capacity of a frozen sparse mixture-of-experts (MoE) model can provide such diversity from one problem prompt, without user-assigned roles, prescribed methods, fine-tuning, or model copies. Agent-Conditioned Routing (ACR) assigns $m$ parallel trajectories persistent, untrained shared/private expert-eligibility masks while preserving the learned, input-dependent token router. On a screened 126-question multi-mode mathematics and physics benchmark, with model judges reading the reported derivations in full, we count the number of problems yielding at least two distinct primary methods among soft-correct solutions in four trajectories. ACR reaches approximately twice as many such problems as the strongest temperature setting under GLM 5.3 (37.3 versus 18.7), and 1.67 times as many under GPT-5.6 Sol (45.00 versus 27.00), at matched output budgets. A blinded four-expert audit on a stratified sample of 30 problems also finds more multi-method solutions with ACR on both backbones, with lower correctness. Matched-eligibility ablations show modest multi-method count advantages for ACR, while token-resampled masks attain higher correctness. An informed sequential prompt elicits more diversity still, using previous solutions and explicit requests for alternative methods. ACR adds about 160 KiB of mask state. In a three-problem microbenchmark capped at 1,024 tokens, its latency and peak VRAM usage remain within 3% of batched temperature sampling.

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