Can we adjust the number of picks required per tournament? For example, more picks for the Majors?

Yes. However, it can't be set up for each tournament ahead of time.

If, for example, you want to have 2 picks for the Masters instead of the usual 1 pick per week, you must change the pick setting immediately after the tournament preceding the Masters ends. Then, once the Masters ends, you must change it back.

You can go to Commissioner Console --> Edit Pool Settings --> Pick Settings and change the number under. 'Players Picked Per Week'