Yes, you can mix metals in a bathroom. Done well it looks collected and designed. Done without a rule, it looks like you ran out of one finish.
The rule: wet things match
Everything that touches water is one finish: the faucet (tap), shower, tub spout, drain and toilet handle.
A second metal is allowed only on dry things: the mirror frame, the lights and the cabinet pulls.
That's it. One finish where the water is, and an optional second where it isn't. (A Decorwick rule of thumb, but one that works in almost any palette.)

Two metals at most
Brass and black, nickel and brass, chrome and black. Three finishes in one small room starts to look accidental.

Buy the wet fittings from one collection
"Brushed brass" from two makers is two different colors. Buy the faucet, shower set and drain from one brand's collection so they match exactly.
Hard water? Choose brushed
In hard-water areas, brushed and satin finishes hide spots. Polished chrome and matte black show every drop of limescale.

Unlacquered brass changes
Unlacquered brass darkens and spots as it ages. That's the point of it, and many people love the patina. If you want it to stay bright, choose a brushed or lacquered brass instead.
Mixing with brushed nickel
Brushed nickel is a cool, quiet finish. It pairs well with matte black on the dry pieces, or with a warm brass mirror and lights if the tile is warm.

Mistakes to skip
- Faucet and shower in different finishes.
- Three or more metals in a small room.
- Matte black or polished chrome in a hard-water area, if you don't want to wipe it daily.
FAQ
Can you mix metal finishes in a bathroom? Yes. Keep everything that touches water in one finish, and use a second metal only on dry things.
Should the faucet and shower head match? Yes. They're both wet fittings, so they should be the same finish, ideally from the same collection.
Do cabinet pulls have to match the faucet? No. Pulls are a dry thing, so they can be the second metal.
Metals chosen for every palette
The Bathroom Decision Map, No. 05 in the Decorwick Measured Home Series, gives the metal finish with each of its 30 palettes, so the faucet, mirror and lights are already decided. See The Bathroom Decision Map




