All my ideas and some thoughts on it:
Not sorted, just a brain dump.
(higher means not it will be implemented first.)
(maybe some of these ideas will not be implemented at all.)

cooldown

send your be to a calculated cooldown after a fight.

dynamic cooldown

will be calculated by a win/lose and maybe your total number of owned bes.

cooldown after transfer in upland

maybe i will implement a detection routine to prevent moveing bes between players to gain any sort of advantage.

stats on bes

Health, Strength, Agility, etc. will take impact on battles

be level

be will gain experience and you may choose which stat to boost with every levelup

hide be details

only show the owner and the be level, not the stats before a fight.

train your bes

send you be to training ground to increase stats. will use experience points and takes it into a cooldown. maybe separate dev-shops for different trainings? training will take some upx to invest

group be fights

send 3, 5, ... BEs as a group to a battle. bonus will be applied if from same collection.

close escrow/tournament containers with be swap

any open escrow containers should be closed, if we detect a new owner on an existing be.

be levels

be will level up with exp, difference of levels may add a bonus to to lower one or a weakness to the higher one

battle companions

take your totem with you to your fight to get a helping hand