Sometimes I find or can see that I can buy a piece of clothing that has multiple effects on it, most notably "X0% magicka regeneration increase and 12/15/17% magicka cost reduction for [school] spells".

When I Disenchant such an item, I learn a new enchantment as normal. But what I'm wondering about... does this count as one single, or two enchantments? If I have 100 Enchantment and the last Perk in the tree, can I enchant a single piece of clothing with "100% magicka regeneration increase and 17% magicka cost reduction for Destruction spells" twice?

(Note: I have no idea if the above Enchantment actually exists with those exact percentages.)

It counts as one enchantment when you use it yourself.

With 100 enchanting you can enchant a robe (only armour slot) with that enchantment, plus one to further reduce destruction casting cost.
Youll notice that the reducement of the first enchant will be less than that of the second.
You cannot use the same enchantment on the same piece of gear twice.
So you can put reduce cost + fortify magicka regen and one to reduce cost only. Or one with the double effect + any other.