I had a similar problem recently with my living room and my contractor recommended "West-highland White" by Sherwin Williams. It is not pure white, but I cannot tell what cast it has. He said it goes with everything and now I believe him!
Shaker beige is beautiful. I know a lot of people who use BM like cloud white, but I personally have not used that one.

I used BM Swiss Coffee for all of my trim. It looks white against my soft neutral wall colors that are shades of beige and taupe, but is actually off-white.

Here is a link that might be useful: Swiss Coffee

I love BM Vanilla Ice Cream. So far, it's gone beautifully with every color I've used in my house.

I use SW creamy. I really like it.

I just decided on SW Kilim Beige for our wall color. We are going with SW Alabaster for the ceiling and trim. It is white but not a bright stark white. I wanted a white that wouldn't look dingy with our our white outlets, switch covers, HVAC, etc. What did you end up choosing?

I just had all my trim painted BM Simply White. I love it! The paint chip will look slightly creamy when compared against the bluer whites, but it's definitely white. It's a crisp fresh white in all my exposures and light levels. It's nice with both warm and cool colors.

Another vote for BM's Simply White. I have white walls, black walls, gray walls and formerly tannish walls, and Simply White works with all of them. It's just a nice, warm white. I'm also a fan of Dover White, although I've never used it for trim.

When I first started researching paint, BM's White Dove was the go-to color for trim. I've never tried it, I'm just throwing that out there. It had the reputation of going with anything.

I have all white woodwork, windows and doors and they are all in SW Dover White and wonderful. Most of the colors in my home are from the BM Historicals and the pairings are fine.