I did something similar when I negotiated my first job after grad school. I responded to the initial offer with: I can start on ___ date for $___/yr (more than

I did something similar when I negotiated my first job after grad school. I responded to the initial offer with: I can start on ___ date for $___/yr (more than the initial offer), they countered about a tad lower than what I asked and I accepted. Seemed to work well. I didn't have multiple offers but had a year left on my current post-doc contract so I didn't need to go anywhere right away.