Hi there, fellow MA resident :)

I would keep the first floor one color or perhaps 2 that played well together. Bathrooms can be different, though, depends on their style.

I'm a big fan of picking neutral shades like greige and then adding color & interest to each room with artwork. That is, I like the way that looks in houses on Houzz - I haven't figured it out 100% in my own life.

Upstairs I would not worry about tying it all together too much - the hallway should relate to the 1st floor & stairwell, but the rooms can be pretty different. Especially if you have kids who inhabit each room. We use our 2nd floor bedrooms as office space (no kids) and even so, the look of each office is different for my DH and I. Mine is more eclectic & travel-related (I travel a lot for work) while his is more whiteboard & bookcase themed (the man never met a book he didn't NEED).

Sorry I can't be more help - wishing you plenty of rain today to break our drought!

You would probably get more input if you post this in the Home Decorating forum.

That said, my opinion is that it depends on the layout of the house. We've got one color (it's a beige/tan) in most of the downstairs living areas because they all connect. The foyer is a lighter version of that and continues on the 2nd floor hallways because it's a 2-story foyer. LR and DR are separate rooms with trimmed doorways, so they are a 3rd color (pale olive). All our bedrooms and bathrooms are a different color. So we have 12 colors total.