Yes, but if you opt to self-publish, you will have to pay a largish sum up front for the permissions on copyrighted music, since they don’t like writing contracts for a small number of copies.
This is where you start researching the copyright holder:
http://www.mpa.org/copyright_resource_center/
And be aware there are two different kinds of permissions:
1. Permission to arrange–this is ONLY legal permission to alter an arrangement for your own performance, not to publish print copies of that arrangement.
2. Print permission as a work for hire. That’s what you will need.