Acoustical research suggests that the listening room's floor reflection is the one most damaging to imaging and staging. For years I have treated the floor reflection by laying flat foam over the carpet on the floor between the listening position and the speakers. The problem with such foam treatment is that it usually must extend fairly close to your feet (at least if you listen in the near field as I do) and thus creates a trip hazard in the room, especially for getting in and out of the listening chair.
Robert E. Greene (REG of TAS) recently suggested placing the sound absorbing material in a vertical orientation rather than covering the floor with it as I have done. This is an excellent suggestion. It may have advantages over the foam-flat-on-the-floor method I've used for decades.
First, it keeps the floor clearer of trip hazards. Second, foam or fiberglass is more effective in absorption if it is standing in free air. Third, you'll need less sound absorbing material this way, or at least you should use less to keep the top of the "barrier" low enough to keep it from interfering with the direct sound from the speakers.
Of course, you could drape heavy cloth material over a stand as REG describes for free. That may well work just fine. But without trying it, I would worry that the stand structure might have some residual reflectivity even if covered by the heavy material.
The 4-inch thick flat foam I use is ideal for this experiment since it is square on the edges and thus is quite stable for free standing a, say, two-foot-by-two-foot slab on edge on the floor.
To figure out where to put the foam, place a small rectangular flat mirror (I use a 4" x 6" version) on the carpet between you and the speaker with the long axis aligned between the speaker and the listening position. Then arrange the mirror so that when you are sitting in the listening position you see the tweeter and midrange reflected symmetrically along the long axis of the mirror. Then place your acoustic foam/fiberglass slab between the listening position and the speaker so that it is normal (at a right angle to) to the mirror at a spot which totally hides the mirror from your gaze when you are sitting in your listening position. Repeat for the other speaker.
To do this as I describe you need acoustic foam or fiberglass which is stable enough to be free standing on carpet. I know that traditional Sonex wedge pattern foam is not stable enough to do this. But the Alphasorb Flat Foam I currently use definitely is stable enough, at least in the four-inch thickness. This foam is both very light and very stiff and that makes it stable standing on edge in a two-foot-by-two-foot slab. See: https://acousticalsolutions.com/product/flat-foam/
This costs $300 for a box of six sheets. You'll only need two sheets to treat the floor. You could use the rest on the ceiling or walls, or share with a friend or two.