There is no across the board answer for how much a normal cat should pee.
Size, wet or dry diet, health, etc. all factor into how much urine will be produced. You can see the effect of those things on yourself. More liquid means more trips to the bathroom. Its hard to tell when you have multiple cats, even just two.

Any time you have more than one cat, there should be one litter box per cat. If you female is not getting to a litter box for long periods because the new cat scares or intimidates her, she can wind up with problems. If she doesn't resort to urinating on the carpet somewhere hidden, she could wind up with a urinary tract infection from retained urine, the bladder can be overstretched re
sulting in a bladder that is less than normal function.

If she isn't getting to a litter box during the day, I would be concerned that she may also not be getting to her food and water. You can check her for dehydration by gently lifting the skin on her back and seeing how fast it returns to normal. If it just snaps back into position, as yours would if you tented your skin, she is not dehydrated. If the skin goes back down slowly or not at all, she is dehydrated and you need to call your veterinarian.

As Dr. Smith pointed out, cats are territorial, and your cat may not want to use a litter box that smells like a strange cat. Depending on how shy your female is, it may take a while for her to become bolder, or she may continue hiding for months. Prior to bringing the new cat in, your cats had a pecking order that they had established. When you add an additional cat, that pecking order has to be re-established all over again. Cats are generally not social animals and though there may be two that are close, they don't have packs or herds etc. Lions live together in prides, but besides lions, you don't find a bunch of cats that move together as one. Because they are more solitary by nature, adding a new cat is stressful. That doesn't mean you can't, you just have to take that into consideration.

Sam

Dear blessings...
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I look at it this way... if a kitty/cat is peeing too much then we need to firstly think about the age of the cat (kidneys?) or the territorial position of the cat in an environment with other cats (natural marking). In your situation ( maybe I'm wrong ) I would think about the territorial situation.