The power move is to have an offer in hand and then tell your company that you're considering leaving for <reason>, but you'd like to give them a chance to beat your new offer by <increasing salary to $X, resolving reason X with a team move>.

Some companies will flat-out refuse to negotiate in this way as a matter of policy, and some will really appreciate you giving them the opportunity to bid to keep you; it really depends on the company and their comp strategy. I think as long as you're earnest about the conversation and don't try to run a bidding war, most companies won't burn bridges with you over a round of negotiations in this fashion.