Yes, this is possible.
The only thing that is not possible is lining up two cards of one player in the same team.
Please note however that not all cards are eligible for every league. The scarcity of the cards also plays a part in this.
For example: if you own two rare cards of a player from Real Madrid, he can be used in both the Global League division 3 and 4 and the Champion Europe Division 3 and 4.