Apple - Scaling different amounts on each axis in Keynote

I don't think you can do it through the usual Actions applied to the object, but you should be able to get what you want using Magic Move.

Get your slide the way you want it, then duplicate it.

In the second copy, scale the object to the new stretched out size (deselect Constrain proportions to stretch the vertical axis).

Then click back on your first slide and in the Animate tab, choose Magic Move.

When you play your slide and go to the next, it should scale your object to its new vertically stretched size.