It is possible! You said you're using the same background and objects for each level right? And when the player goes to a level, you want to set the animation of those objects accordingly?
You would just have to do something like
On levelbutton.click
- Go to level levelbutton.number
- Set bacground animation frame to levelbutton.number
- Set objects animation frame to levelbutton.number
You'll might have to pick the objects using something like "System - pick all objects" so all their animations are set to the same frame as the level you picked.