When you get Pet Training, you normally can't train more than 3 pets. When asked to choose a pet to discard, select "Raise Pets" option [center option on left side]. After it you will be able to select option to train another pet. You can train all possible pets this way.
First, go to Mel Senshir and save your game. Then, kill the Dokkalfar merchant to the left of where you spawn. Pay the fine or go to jail, then go to one of your houses and sleep for 4 days. Now return to Mel Senshir and the Dokkalfar merchant you killed will have respawned with fresh inventory. Purchase a new backpack and repeat for an unlimited supply of backpacks.