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An ability that advances a Class to a higher level is a normal activated ability. It uses the stack and can be responded to.

Class cards have multiple text box sections. Other than the top section, each section contains a class level bar that includes a cost and a level number. Each represents an activated ability with the listed cost that advances the Class to the level listed in that bar.

Each Class starts at level 1 and has the abilities in the top section of its text box. Once a Class advances to level 2 or level 3, it has all of the abilities listed in the associated section of its text box as well.

Gaining a level won't remove abilities that a Class had at a previous level.

There's no restriction on how many Class permanents you can control, whether they're the same or different classes. Each Class permanent tracks its own level separately.

You can't activate an ability that advances a Class to a particular level if that Class is already that level or higher. For example, if a Class is already level 2, you can't activate the ability that advances it to level 2 again.