Referencing https://dev.mysql.com/doc/refman/5.7/en/create-trigger.html ,
As of MySQL 5.7.2, it is possible to define multiple triggers for a given table that have the same trigger event and action time. For example, you can have two BEFORE UPDATE triggers for a table. By default, triggers that have the same trigger event and action time activate in the order they were created. To affect trigger order, specify atrigger_order clause that indicates FOLLOWS or PRECEDES and the name of an existing trigger that also has the same trigger event and action time. With FOLLOWS, the new trigger activates after the existing trigger. With PRECEDES, the new trigger activates before the existing trigger.
Before MySQL 5.7.2, there cannot be multiple triggers for a given table that have the same trigger event and action time. For example, you cannot have two BEFORE UPDATE triggers for a table. But you can have a BEFORE UPDATE and a BEFORE INSERT trigger, or a BEFORE UPDATE and an AFTER UPDATE trigger.
With that, can Percona toolkit now operate appropriately with tables that already have triggers?
Percona Toolkit v 3.0.4 is planned to be released this week and pt-online-schema-change has a new parameter, --preserve-triggers to keep already existing triggers.