How many colors allowed?

I'm planning to paint my boring white walls, and I'm looking for some guidance on how many different colors is considered appropriate in a house. The kitchen is going to be red, but everything else will be fairly neutral, variations of gold, tan, green, etc. I don't want to paint all the other rooms the same color, but I also think if I paint each room a different color it'll look too disjointed and won't flow together well. So what's the happy medium? How do I decide which rooms ought to be the same colors, which ones can be different, etc?

Here's the layout of the house if it helps:
Upstairs, rooms connect in the following order: Family room, kitchen, dining room, living room. And there's a hallway that connects all of those rooms, plus a little half bath in the entry. You can see the kitchen from all the rooms except for the half bath. You can't see the family room very well from the living & dining rooms. And the living and dining rooms are pretty open into each other, but there are some small walls that provide enough separation that I could easily do them in two different colors if I wanted to. I don't want any of the rooms except the kitchen to be red, but I'm not sure how many other colors to use, should I paint all the other rooms the same color, or can I paint them all different colors and still have it look good? Up here I was thinking shades of gold/tan.

Downstairs, I have 3 bedrooms, then a hallway that connects all of them as well as a full bath and the laundry room (which probably isn't getting painted). I definitely want the master bedroom to be green, but I wasn't sure if I should do the other bedrooms green too, maybe different shades? Or should one or two of them be the same as one of the upstairs colors to unify upstairs/downstairs?

I appreciate any advice! I know how to find multiple colors that go well and coordinate with each other, but I don't know how to get the balance between being boring and painting all the rooms on one floor in one color vs looking too disorganized by painting each room a different color.