sure you'll have white, gray, black, dark brown, medium brown..make sure to repeat them all a bit, in small touches, different textures. a bit of white in your living (a throw? a mat in an art? part of a pattern in a rug or throw pillow? a vase?), a bit of brown in the kitchen (a wooden bowl,a cutting board?)..small stuff like that bring plants-there, you have green..:) which miraculously goes with everything, gives a feel of being both warm and cool, and doesn't prevent you from using any other color out there be it two accent colors or twenty other two-pick your favorites. Every color has hundreds of shades. I'd pick warm colors in cooler shades..or vise versa..since your existing colors are cooler, you want to bring some warmth in but not to steer too much into very warm territory. you also have sharper, cleaner colors..doesn't mean all your colors should be like that, one can be pretty free with small accents, but keep most of them same amount of "mutedness".. and if you like contrast I'd go for shades a bit vivid..not too pale say if it's yellow-rather daffodil than amber if it's red-rather geranium than red brick if it's blue..here, I'd consider depth of color too..something deeper. teal, cobalt? not too light a blue.. in short..repeat what you've got..bring textures..metallics if you like them ? wicker? something knitted? and then start introducing colors you love. chances are you already love the shades that'll go with your place..you picked clearer colors-means you love clearer colors..I, for example, always pick smth muddier, so chances are I'd continue to do so..:) and then if down the road I want to steer away just a bit, in a little something like art or vase-not a problem...once I know my general direction, I can start breaking my own rules here and there...:)

@Jennifer K I was treating the charcoal as a neutral, but, now when you said it, it does feel a bit weird having two strong dark colors (navy and charcoal), so I think I will go with the charcoal only. Coral actually doesn't look bad at all! Old brick fireplace was my husbands wish, I like it too, but my problem is that I don't know how to handle it, since I am not at all "red person", and I am really bad in decorating with red. Kitchen is 90% done, and hopefully would feel similar to those (only with oak flooring, and brick from the back of the fireplace):

This is what the living room looks like

I favor traditional furnishings too! I would go with a hand made, hand-knotted Persian carpet every time. Even if it doesn't have your stated preferred colors, a Persian carpet will fit in every decor, and many of the Persian carpets do have more subtle colorways. For example Nain, and Isfahan. Just keep your eyes peeled, and don't be in a rush to buy. Quality in craftsmanship is most important in a handmade, hand-knotted Persian carpet. Don't settle for a cheap imitation. These days the market in Persian carpets has sunk to abysmal lows. That is great for the American buyer.