We use cranes very frequently. On crane days we pack in as many crane jobs as we can to get the most use out of the crane. They charge hourly, and will go to as many sites as we wish, as many set ups as needed.
So, short answer is yes. It is common practice to use a crane on multiple jobs in one day.
Company we use charges a 4 or 5 hour minimum, so we use them all day if we can. Even if it's a tree we could climb & rig, the crane just saves hours and hours of labour on the big stuff.
Side note, be careful if you're doing the ground work with crane picks. Not only can the log roll unpredictably, but just last week I was nearly struck by a pick when it snapped in half where it was strapped on.
We had the butt of the piece on the ground, and I was guiding it to lay the way we wanted it. Snap! The log thumped to the ground. I looked up and saw the other piece still on the strap up in the air, swing in my direction.. it grazed me on the arm lightly, just barely missed me. Dang that was a fright.
Stay safe my friends!