Can I keep more than 15 players?

You can specify any number of keepers from 1 all the way up to your league's maximum roster size (40).

To increase your roster size and keepers, first go to League » Settings » Edit Roster Requirements » Custom. Then click the edit button on the Total and Bench line. Then go to League » Settings » Edit Keeper Rules and select the number of players you want owners to be able to set as keepers.