When switching Monsters out in battle, switching to a Monster of the same attack-type (Physical Monster to Physical Monster, Magical to Magical, etc.) will add a level to your Stockpile Gauge.

Failing to keep switching and maintaining the chain will cause the stockpile to deplete to zero, however, if your final action to end a chain is an attack, that attack will be highly boosted by the stockpile you've built up.

Along with boosting your next attack, the six levels of stockpiling can have other effects as well, such as boosting your stats, lowering your opponent's stats, or inflicting status effects. With six levels you will need to be sharp and choose the right amount to build for each situation!
There are rumors of a sacred technique that allows you to go beyond the sixth stockpile, however, no one has ever reached that level of mastery over their Monsters in battle yet...
Who knows what could happen?