Some version of mushroom or taupe might look great with your walls and still read as a neutral so as not to limit your accent color choices.

Thank you forhgtv, do you have any particular colour in mind, especially the mushroom because I think of Bleeker Beige as a taupe. If I am wrong and being in year one of colour, please correct me.

Puce!!! I just painted my front doors puce (the dark brown purple variety) I love it because its sort of a non color that makes a statement without talking too much.

Here are a whole spectrum of colors that you might consider.

Here is a link that might be useful: Canadel wood finishes

I didn't have a specific color in mind. Normally, I think of mushroom as a darker taupe with more blue or gray in it. I was thinking that you could pick a color that gives you a little bit of contrast to the wall color, but not a lot. Of course, you could literally paint the furniture the same color as the wall, but in a high gloss. That could look good, too. Another option would be to use a brown or bronze glaze over your current white paint.

How about a darkish shade of green?

I also thought of a green that is almost black after reading your description. You could also choose a coral color for some pop or a wild aubergine.Eggplant is an elegant choice as well, but you want to make sure it is really dark. Paired with chrome or polished nickel hardware, it would really be stunning.

What about a really rich charcoal color? Something warm, not an icy grey? Then use polished nickel hardware.

You could also paint the case of each piece in a color two or three shades darker than the walls, and do the drawer fronts in an interesting, but neutral, wallpaper or fabric.

Another choice is to find a common color that shows up in your rugs and accessories, perhaps a certain family of green tones, and paint the pieces in that green. Green is a great neutral in nature, and would do the same for you here, but bring a touch of color and interest to the room.

I was thinking immediately, a non-primary shade of navy or a gray!

I also like the idea of a darker shade of the walls.

How cool. I'd like to see pics of the pieces, no matter what the colors!

C.

I had dressers painted the same color as the walls, but in a high-gloss finish. It was beautiful. The color was midnight blue. If you want an alternative to black, midnight blue would be nice.

I just used SW plum brown in the powder room and I love the richness of that dark color.

I would love to see the pieces as well, I'm sure they are a treasure. What's the wood that they're made of like? Instead of color why not strip them and bring them back to their natural beauty?

Sorry for my delay in responding, but with today being the last day to file income taxes and federal election day here in Canada, I have been busy.
Thank you all for your suggestions. jterrilynn is your puce colour similar to the SW Plum Brown that amj0517 mentioned. I really like it. Les 917, a rich charcoal would be lovely, too. Do you have a BM colour in mind.
For the summer I use a natural seagrass type area rug which is banded in black. For the winter I usually use my very old/antique Persian which reads mostly a raspberry red but also have some blue, gold, and a tiny touch of green. That being said, it doesn't mean I'll use it this fall, although I should because it has been valued fairly high. The artwork and other accessories are not so much an issue because they are easily changed.
I am not putting up pics of the furniture because it is nothing special. Just a maple dresser and chest that I have had since childhood and certainly not worthy of stripping. (Actually, I don't know how to upload photos here.)
This room was just spring cleaned today (not by me) and I am 'trying' out different colours using throws, sweaters, towels and anything else I can find LOL.
Sorry for being so long winded. I guess it's down to a dark purplish brown or charcoal gray, I use BM so colour numbers that correspond would be helpful.
Again, thank you all.

Silhouette is an Affinity BM dark grey. AF-655. It leans more cool to my eye.

amielynn, thanks for that info. I really like that colour and will pick up chips tomorrow.

You are very welcome :^) glad to help, hope it does the trick!

AHHHHHH, I went shopping today. Perhaps it was the wrong time of year because all I saw was in fresh spring colours. Now I am really confused. This is not only about my dresser and chest of drawers because, for now, I have decided to paint only the tops and in a glossy Bleeker Beige (thanks for that ides). Now, I am confused about the bed and bedding.
I always had a dust ruffle, but don't want it anymore. I am seeing that many people now just put a fitted sheet over the box spring. Does anyone have any comments about this? If I do this should the covering on the box spring match the sheet set or the duvet which is white? If it matched the sheet set, then it would need to be changed often!!!, right?

Please tell me the rules/ideas of dressing a bed when one does not buy a set.

I like the new fashion of a duvet folded at the foot of the bed and a coverlet on the bed, but don't know what should match with what.

HELP

Thanks