I've seen this management request before. Typically it comes from the frustrated Product Owner who projects the current velocity against his "desired release scope" and is frightened by promises he has made to customers. He understands the new system and velocity, and decides to use the "whole team" concept to suddenly include you in the problem. Next thing you know, he's standing over the team asking for "more velocity!".
Feels like the old way of working again, doesn't it? Agile doesn't solve the problems you felt under waterfall, it simply exposes them in a big ugly way. You can either cave and play the old games, or you can hold your ground and help management become agile with you.
Here's my sarcastic advice to Alex:
Your gut is telling you the right thing... you don't forcefully "increase velocity", you have to help your team get what they need and it will increase on its own over time.
The easiest solution is to start accounting for the velocity of vacations and conferences or training. These are guaranteed points and therefore will drive up the average. After a few sprints of the higher number... disclose that you've gamed the system. Then drive home that forcing metrics only forces gaming of the system. Remind them that this is why waterfall fails in most environments. They are only pushing you to go back to the old way of doing things under a new name.
Help your project sponsor become agile!