It depends on the contract you work under and how many days you work during your reserve period. My company maintains a higher level of reserves than most, so it's not ususual for those guys to not work too hard. If there are open trips, a guy could pick them up on his days off. Like I said about the contract, some airlines have limits on how much extra work you can do. Our limits are pretty high. I think the cap is 196 hours in 56 days, when our normal pay for that time frame would be 150 hours. A three day trip is worth about 20 hours, so you could pick up an extra three day trip every four weeks.
A lineholder can do it, too. My basic rule is that I don't do extra flying unless it happens to be a VERY easy trip. One where I get paid for three days but only work one because of the deadheads. The trip would also have to be close to where I live.
Some guys never pick up open time and others LIVE off of it. Another bad thing about working extra is the company loves it cause they don't have to hire more pilots.