So far everything is neutral so if you’re trying to stay within the neutral you’ve got going on you’ll need to add lots of tone on tone texture and beautiful elements done in glass, iron, etc for decor. I would go all out in textured pillows and a chunky throw or two. MagnoliaHome brand at Pier 1 has great pillows. I have several from this line for our living space but I did replace the insert with a down fill one for a better ‘smoosh factor’ ;). https://www.pier1.com/on/demandware.store/Sites-pier1_us-Site/default/Search-Show?q=Magnolia home pillows

I'm guessing that one of you inherited grandmother's home, and you moved your own casual slip-covered style sectional into it. That explains the total contradiction with the drapes, tables, rug and mirror. It is a very large rug; maybe too big for a bedroom if your home is small. I see why you like it; the colors are appealing, but I doubt it has much value. Certainly worth finding out, but my own experience is that no one will pay you what it is worth. My 5x7 Qum was purchased in the 70's for $2,500. Appraised at $5,000 in the late 80's and can't get $800 for it today, although the original appraiser said it should be worth $10,000+ by now. Depends on where you are and who might pay for it, if you decide you're not keeping it. If you intend to keep all the original furnishings of the home, you should probably plan to style new purchases to fit in well with granny's stuff. Otherwise, you could have a "living" estate sale and get rid of the items that have no real sentimental or high $$ value to you.

This is what my family room looks like now

It's not that I'm good, it's just that I'm from Jerusalem))(amongst other places I'm from) Iznik is one of my favorite patterns ever, so at some point, I learned the name already. It is indeed Turkish, and I on't have it, but I dream of having it. I even found sconces with Iznik pattern on them on Etsy, I just don't need them but got very excited that somebody actually makes them(also in Turkey, I think) I'm into patterns-ceramics, fabrics, you name it. I have too many, and am in love with many more. We also have a small plate from Armenian quarter-exactly same flower design. My DH surprizingly loves ceramics and dishes, so it's something we share and love hunting together. Our tradition is to always bring something from Jerusalem, and something in 99, 9% is ceramics. I also have a corner dedicated to all the art I bought in Israel during the years. I missed on "my" perfect Jerusalem piece many years ago, I though it was too expensive-and I'm looking in vain since then. Everything I love to the point of no return, is much more expensive than that painting was.. I love your collections, and wouldn't hesitate to borrow from them whatever you might like to borrow. Whether color, or pattern, or idea, or just a hint on something that is hard to describe but is there-and only you might know what it is.