You will typically not be able to negotiate with senior lienholders.
They hold all the power and will have to be paid in full if someone junior to them is foreclosing. You might be tempted to say to yourself, “If the junior lienholder is foreclosing, and the property will still be subject to the senior lien, then it must be worth at least as much as those two debts combined.”
This would be a mistaken assumption. Never assume someone else knows more than you and never base your decisions on that assumption. If you cannot justify the value from your own research, do not let other parties’ possibly foolish decisions sway your opinion.
You generally do not need to negotiate with junior lienholders unless there is substantial equity in the property. In that case, you want to avoid their possible exercise of a right of redemption after foreclosure, and you want to avoid a bidding war at the foreclosure auction. Remember that virtually no lender wants real estate, they want cash.
If you are worried about junior lienholders, remember that they are worried about owning a house. In particular, they are fearful of good money chasing bad, and having to pay off a senior lienholder in order to acquire real estate so they can possibly sell it and then recoup their losses.
That is a lot of risk for them. Knowing this, you can negotiate with them to accept less than their full claim.