The packaging and instructions show that you can. You just keep linking as many as you wish together and have fighting tournament. When the pets fight, you have no interaction with them, you cannot select any fighting technique or control any weapons. You involvement is only in the care and training of your fighter. I think the pets would be more interesting if the user had some level of control of his fighter during the fight.
Some pets have a very poor timekeeping.
These pets kept good time for several days of testing. You must give it medicine twice. Once now and one more time at least 10 minutes later. I started the pets one morning and the next morning they seemed to want to sleep all day. It was about 5pm by the time I figured out they were sick and needed medicine.