It's always possible. How much is involved depends on how high you want to go and how much space you have. In a small space where you want to increase grade by a lot, you'd need a retaining wall, which will add to your costs. If you have a lot of space, you can raise it gradually, but that would take more dirt.

And you'll know from your excavation how much trucking of dirt costs in your area.

We're having to raise our grade a little in order to keep water from draining into the neighbors yard.

Costs will vary with local circumstances. If a grading contractor must buy fill dirt and move his equipment to that site for loading, it will be quite expensive. I found a contractor who was working on a job and needed to get rid of excess dirt in a hurry. Lucky me got it for just the hauling charge, the other customer paid for the loading. Honest contractor.
For your job, sounds like a Bobcat could do the grading at your site after the fill is delivered there.

You should do it. If your builder/grader doesnt know of any fill-out jobs in your area, I would make an effort to reach out to others that may know of some.