Could you fit boxsprings under an Ikea daybed?

There is an Ikea daybed that I’d like to do a few adjustments to. I’m in the market for a new bed and I’ve always enjoyed daybeds, but I’ve currently got a full sized mattress and box springs I’d like to use.

This model can be a single or a double, as the bottom level pulls out. Using my full sized set, I’d be using it pulled out in the double size. ( photo: http://is00.thegumtree.com/image/big/83888804.jpg )
And here is a link to the bed online, with the measurements. : http://www.ikea.com/us/en/catalog/products/30080316/

What would be the best way to tweak the model to make it fit the full sized mattress and boxsprings I have? The website suggests that you buy a thin mattress to go over the slats, but I’d rather use what I have.

The finished project should look something like this : http://img14.imageshack.us/img14/3088/2359410663c622f9af08z.jpg

Do you think that I could take out the wooden slats along with the drawers and fit the box springs in the bottom level comfortably? Perhaps putting in the drawer fronts for esthetics?
I’m not very practiced in putting things together, so I’d really appreciate some help.

Here is a youtube video of the bed, showing the drawers that I was mentioning earlier, and couldn’t find an example photo of :: http://www.youtube.com/watch?v=rKjrdSkdvCg (10 seconds long.)