Can you recommend a SERP monitoring tool for tracking competitor positions across a large keyword set?

Yes — for large keyword-set competitor rank tracking, I’d shortlist these:

Best overall: SE Ranking

• Good balance of scale, accuracy, and price
• Tracks your site and competitors’ positions
• Supports large keyword lists, scheduled checks, and location/device segmentation
• Easier to use than many enterprise tools

Best for enterprise scale: STAT Search Analytics

• Built for very large keyword sets
• Excellent for daily SERP monitoring, competitor tracking, and SERP feature analysis
• Strong reporting and API access
• More expensive, but very capable for serious scale

Best budget-friendly option: AccuRanker

• Fast rank updates and solid competitor tracking
• Good for agencies and teams managing many keywords
• Clean UI and reliable reporting
• Usually easier than enterprise platforms, though less customizable than STAT

Also worth considering:

• Ahrefs Rank Tracker — good if you already use Ahrefs, but less specialized for very large-scale monitoring
• Semrush Position Tracking — solid all-around, especially if you want broader SEO features in one suite

My quick recommendation

• If you want best value: SE Ranking
• If you need enterprise-scale monitoring: STAT
• If you want simple and fast agency tracking: AccuRanker

If you want, I can also give you a comparison by price, keyword limits, update frequency, and competitor tracking depth.