I 'll tend to agree with what @solarflare saidwhat @solarflare said.
It won't come off nicely for sure if you want to push for more after they already provided what you wanted.
Moreover, consider it a lesson learned. If you 're not in a dire need of a job and you think you 're in demand next time aim at the higher range (or exceed it if it's not that realistic!) and then you have leeway to play the counter game or who knows they might really like you/need you and even give you the higher range salary from the get-go. If there's something you should keep from this, is to not be afraid to lose agreeableness, you won't receive something unless you ask for it and no company will turn down a good candidate just because they price themselves highly(but still competitively for the market).