I actually read last night why you pee more as your body is getting used to the intake. From what I read, its your body letting go of its stored supply of water, because it starts to rely on the fresh water coming in every day.
Alot of people think the water is going straight through them & give up after a few days because of this, thinking its not working.

I've done 2 days now with just plain water. I'm back to a coffee or 2 a day, but as I've said, for me & my body that is a huge deal. Just the water intake on top of other drinks is going to be a good thing for me. I know water comes from everything you eat & drink, but everything I was drinking included sugar & all sorts of other additives. I'm not against coffee & caffeine. It has its benefits, as does tea, with antioxidants etc.

Any amount of water for me, with or without coffee, is going to have huge benefits compared to before.