Company requirements aside, you can do whatever you want in your off time, even during your rest period (check my reference and tell me I'm wrong) as long as you're adequately rested for your assignment. Just as long as it's not 121, 135, or 91K.

§117.3 Definitions.
Certificate holder means a person who holds or is required to hold an air carrier certificate or operating certificate issued under part 119 of this chapter.

Rest period means a continuous period determined prospectively during which the flightcrew member is free from all restraint by the certificate holder, including freedom from present responsibility for work should the occasion arise.

§119.1 Applicability specifically excludes pretty much all commercial flying activities you would be doing outside of a Part 135 or 121 operation.

For me, this is a spectacular change to the rules. I was ready to leave Part 121 because I want to have my logbook filled with more than shiny jet time. I still love to instruct, tow banners, give rides, ferry planes cross country, and all of the other things I used to build time for this job. Now I can. Well, that is, if the company will let me. I'm working on that.

"Do you have one thousand hours, or one thousand of the same hour?"