Can I have two different UV unwrappings of the same object? Basically, I have two textures, one of which is mostly transparent. I want to combine them, so that they're one on top of the other.

The problem is that one is bigger than the other, so I would need two different UV unwrappings of the same object, one with a bigger scale than the other.

Is it possible to do so or should I combine the textures in an external program?
Yes, it is possible.

In the mesh panel, under UV Maps, press the "+" button. This will create a new UV map with the same coordinates as the existing one.

For Cycles, in the node editor, select Input -> UV Map to use different UV maps for different shader parts.

In Blender Internal, you can select which UV map to use in the texture panels.