I think you'll have more luck with the Dover White if the room is north facing and gets little natural light. Others can correct me, but I think north facing, dark rooms do better with a yellow undertone white paint than a blue, which is cool and might look drab in a darker room.

You might want to also try BM White Dove, which is a BM 2014 Paint of the Year (white) and painters and decorators love it because everything goes with it, or at least that's what they say. All of the trim and windows and the painted ceilings in my house are done with White Dove, at the ceiling painter's recommendation (I did the rest myself. Ugh!). It does work in all of the rooms. I was surprised to learn it's got green undertones because I've NEVER seen it in any light. It's a soft white. Maybe hold a chip up next to the subway tile.

i am trying to choose trim color now too... our remodeler prefers to use SW ... i am trying to avoid yellowish whites-- our bathroom will be a greige and bedroom quietude (i believe) ... i am considering panda white, marshmallow, creamy, and white duck... i found online someone saying SW alabaster is very similar to BM white dove, but it almost seems to have a too green undertone to me... ? the whites really vary with the light-- i want to do 1 trim color for master bed and bath, and have both north and south windows, so want a warm off white with very little yellow or pink/orange cast...
SW considers snowbound a cool white, but it seems to have very little cool color to it, but it's a brighter white than i want...(i think!)
ugh! :)

SW Extra White works well for trim.

Consider the colors you will use in the room when choosing whites.