Negotiating a subcontractor's rate hike without damaging the relationship

[Savannah.W]

I'm a project manager in the construction industry, and I'm about to enter a critical negotiation with a major subcontractor who is trying to significantly increase their rates due to material cost inflation, which would blow a hole in our project budget. I need to secure a fair price without damaging the relationship, as we rely on their specialized work. For other professionals who negotiate high-stakes contracts, what specific negotiation tactics have you found most effective in similar price pressure situations? How do you prepare your BATNA and opening position, and what's the best way to frame concessions or explore value-added trade-offs beyond just the dollar amount?