Anna, I had one for years that got to be over 4ft. long, with beautiful trailing stems and dozens of 8in. pitchers. That one you have is in a big pot, I would think you could let any stems grow that have green leaves on them. It will be a rampant grower in the warm weather, especially if you keep it in your greenhouse (but open the doors to let in some bugs for it).
The big one I had, I probably should have pruned a bit, and kept it inside the pool cage where I could monitor it. Instead it got too big, so I parked it out in the garden where it got watered with well water, then didn't get enough water through a dry spell in the summer and I found it well and truly expired after that ill treatment. I'm treating this new one much better - they're not cheap, and I really like that it eats up any mosquitoes and no-see-ums that get into the cage.
I also found out recently that you should leave the pitchers on even after they are brown and dry. As long as they are holding water, they will still catch insects and help feed the plant. They do eventually crack and leak, and that's when I cut them off.
(edited to add) I've never tried to root a cutting, but I'm sure as heck going to give it a shot this spring!
