That sounds more like getting ready for a game than throwing a pen. Pre-game, I will throw about 30 pitches once I get up to speed and get hot.
Pre-game: I throw these until I feel right, but no more than 5 of anything except the curve ball if necessary
3-5 2SxsFB (2 Seam eXtension Side FastBalls)
3-5 2SgsFB (2 Seam Glove Side FastBalls)
3-5 low Change up
2-3 high Change up
2-3 xsSL (eXtension Side SLider)
2-3 gsSL (Glove Side SLider)
?? two consecutive acceptable curves (it may take 2 or it may take up to 7 before I get two that felt right and break the way I want)
I focus on up to 3 specific pitches and throw each to its own specific location in any one bullpen session. I don't scatter the ball around in a pen. Pattern is close to 20-20-20 with 5 mins between sets. I'm refining pitches in a pen. In the pre-game, I'm just seeing what I have today that's working right.