Is it possible to produce a stereo effect from more than 2 loudspeakers for example(4 full range driver) placing them one on each side of a square?
Stereo is kind of two separate sound sources. Separation is part of it. Panning hard left or right will be an option, just as keeping the sound source exactly mid centre is. With speakers left/right ( or in this scenario, north/south, the best place to be to hear stereo is in the centre, facing west/east. When there are speakers on all four sides, the stereo image is lessened because the sound from each source is widened. So, with say, left channel at north and east, right channel at south and west, stereo will still be perceivable when you face northwest or southeast.
If you use multi-channel sound, as in some audio-visual amps fot teles, etc., then four speakers such placed won't be enough.
Stereo recording was invented to enable a recording engineer to produce a reproduction of the original performance that emulated what the listener might hear at a live performance. If you attend a performance of the symphony orchestra - from where you are seated in the audience the brass may be on your right and the strings on your left. So a producer attempting to reproduce the sound in the way it might be perceived in that instance - would pan the brass more to the right and the strings more to the left.
Ideally when listening to a stereo recording, one should sit equidistant between the two speakers to get the full stereo effect intended by the producer and engineer of the recording. There is a sweet spot that will give you the full intended effect and any deviation will give you something different. Of course you can listen with stereo headphones and you will always be in the sweet spot with the left hear getting a different mix than the right - but each ear getting exactly what was intended by the producer/engineer.
When vinyl records were the primary means of recording, stereo was the most practical way to divide the music. In the 1970's, there was an attempt to expand the concept of stereo to "quadraphonic" Click here to read Wiki Article - which divided the recording into 4 distinct mixes in an attempt to recreate the effect of room reverberation and capture what a listener might hear bouncing off the back walls of an auditorium in a live performance. What you describe with 4 speakers, would be the speaker placement pattern one would use in a quadraphonic system. I still have a quadraphonic receiver that I bought when that format was originally introduced.
The quadraphonic format was a commercial bust partly because it required 4 speakers and specialized equipment to reproduce. And the sweet spot was even more elusive and impossible to do with headphones. Also, needles for records had to have 4 diamond contacts vs. two and the quadraphonic action of attacking the grooves in the vinyl from 4 angles reduced the life of the records.
With digital recordings now the prevalent form of distributing music for the average consumer of commercially produced music, it is now easy to encode recordings for "surround sound" which can make audio visual productions (such as movies) sound more realistic by moving the perceived source of the sounds to various places in the room - not only from front to back but from side to side. Surround sound is great at creating movement of the sound so that the sound of a jet can begin from behind the listener, get louder and move to the front of the listener and fade to emulate what you would hear if a jet flew overhead. Optimal use of surround sound which will typically use anywhere from 4 to 6 speakers plus a sub-woofer - requires a controlled listening environment where the listener can be positioned so that they are surrounded by the speaker configuration - ideally in the center of a square or rectangle.
But since the brass section in a musical performance doesn't move around as fast as a jet flying over or a car driving by (even in a marching band) - surround sound is not as useful for music reproduction as it is for audio visual productions and again, can't really be faithfully reproduced with headphones or earbuds. So stereo is here to stay. Since we only have two ears, there is really not a better way to reproduce a musical performance.
With all that being said, if you want to use 4 speakers to play a stereo recording, you will want to place the speakers in a manner that allows most of the audience to get the stereo effect intended. Ideally, a listener should hear what the producer intended to put in the left channel, in their left ear and vice versa. All of the sound should come from in front of (or from the left and right side) the listener for stereo - with nothing coming from behind the listener.
Your multi speaker car stereo is more marketing hype than anything else and helps enhance the sound for rear seat passengers. Also, in your car, all the speakers are fairly close to your ears so that what you hear from the rear right channel gets to your ear at about the same time as the front right channel. Plus, multi speaker systems in autos often put tweeters in one location (closer to your ear) and woofers in a different part of the vehicle (where the cavity can act as a resonator for the low frequencies), so it's more about the logistics of using car doors, the trunk and the dash as speaker cabinets than optimal reproduction of the sound source.
Putting speakers in a surround sound configuration such as 4 corners of a square, would defeat the idea of creating a realistic reproduction of what you might hear at a live performance. The echo from the back wall would need to be at a slight delay and much quieter than the sound coming from the front of the listener. So even if you lowered the volume of the rear speakers, the timing would have to be retarded to get the proper effect.
If you wanted to try to make that work (four speakers with two behind the listener and two in front), you might be able to mix your source by using two stereo recordings of the same music through two stereo mixers if you could synchronize the two recordings to get the timing right. If you can solve the sync piece, then you could send a lower volume, slightly delayed signal to the rear speakers through one mixer or stereo amplifier with the main recording being sent to the front speakers at full volume through a different mixer/amp. There are delay effects but they are stereo effects and would be sent to both channels equally. They don't do left/right front/rear.
Good luck with your experiments. Perhaps you can find a way to create a unique listening environment that will wow your audience.