How do I muffle the sound in a great room?

Rugs on the floor, decorative tapestries/quilts on the walls, long full window drapes, "stuffed" upholstered furniture, and wood furniture vs metal.

Soft furnishings. Rug, upholstered furniture, curtains or drapes. Decorative pillows.

Acoustic panels work such as this one: https://amzn.to/2THgpta

Sound from outside, from another room or inside the family room. Things like bookcases with books in them, closets, carpeting, drapery are all sound absorbers for homes.

What is the height of the ceiling? Unfortunately, although grand in appearance, overly high ceilings are often the source of very poor acoustics.

https://soundproofadvice.com/reduce-echo-in-a-room-with-high-ceiling/

https://www.kylieminteriors.ca/how-to-reduce-echo-in-a-room/

Rugs can also help if you have bare floors.

What about the possibility of adding some pony (½ walls) or building a lowered tray-style ceiling in part of the room?

https://www.thespruce.com/reduce-noise-in-living-space-1822844#:~:text=How%20to%20Reduce%20Noise%20in%20Your%20Living%20Space,glass%20and%20can%20be%20self-installed%2C%20saving%20money.%20