You are adding upper cabinets similar to what you would see in a kitchen?

yes

I don't think there is a "standard" for that. I have never seen it done, and I have been hanging out on the Bathrooms Forum for maybe 6 years. Medicine cabinets yes. Deeper cabinets, no. Med cabs, if they are very tall, can start anytime after they clear the top of the faucet.

Yet we see lots of 'tower cabinets' sitting on vanity tops in bathrooms....and the associated problems w/ the bottoms getting wet and the mdf/ particle boards gables getting wet when precautions aren't taken during installation.

The problem that I see with wall hung cabinets is, if the room is small--likely to be because it is a bathroom--then a large cabinet can overwhelm the space. A better approach would be to recess the cabinet into the wall, if at all possible. Or use a shallow cabinet--6" deep, or less--if that will meet your storage needs.

Open shelving would be a better option for a less crowded appearance. Much more common in bathrooms that kitchen cabinets.

Another option would be to put the upper cabinet above the toilet. That's a more typical arrangement

I know this post is already 6 months old. But we actually put an open shelf cabinet in a small master bathroom several years ago (maybe 2012?) I don't remember the exact dimensions but we probably hung the cabinet about 12" above the countertop (gave us more space on the counter and kept the cabinet from getting wet.) Most likely 18-24" wide, 12" deep and about 36" tall since it has 3 shelves (Kraftmaid.) Nice thing about having the sides is it prevents things from spilling over. We did have to fold the towels lengthwise in 3 before rolling up to make sure it didn't overhang the shelves.