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Yes, this is definitely possible with Magento. Might require a little custom coding.
One possible way to do it:
1. create all of your categories
2. build a block that shows all of the categories in the order/groupings you want them in, and understands which category you are currently showing to reflect state
3. modify the left column to pull in this block
Here the link to my website: http://www.shortprint.nl
As you can see I already have a vertical menu. But I want, when the homepage loads, that all subcategories (level1) are shown.
Is there a easy way to do that?