- The energies involved in the firing of 4 57mm projectiles at the same time are surely lower than the energies involved in the firing of 1 152mm projectile since the overall weight of the sum of the 4 projectiles is lower than the 152mm projectile. It means that a platform that resists the firing of 152mm ammunition should be likely enough for a 57-4 configuration. As example the weight of the 2S3 and the 2S5 of 152mm is of 27,5 tons. I can not assure it, but I would not rule out that the Kurganets and Bumerang platforms would be enough for a 57-4 configuration. I would try it.
In the other side, I do not think that the 57-1 configuration would be accepted in the Russian Armed Forces in something smaller or less armoured than a BMD-4M, because the criteria about safety of the crew would be applied.
You are contradicting yourself... first you say the recoil from four 57mm guns does not exceed a single 152mm gun, and so a vehicle with 4 x 57mm guns could be as light as a current vehicle with a 152mm gun, but then you say current levels of protection are not acceptable... which would apply to the 152mm gun armed vehicles you mentioned...
Then, following with the example I tend to think that the most likely situation would be 1000 57-4 Kurganets/Bumerangs vs 4000 57-1 BMD-4M. I would expect the economic analisys to be favourable to the first option.
You are looking at this the wrong way. four x 57mm gun barrels has the only advantage of firing four times as many rounds as a single gun armed vehicle... rate of fire is very important for unguided guns of small calibre like 23mm or 30mm cannon because the more projectiles you get into the air the better the saturation of the area where the target will be is denser making for a better hit probability.
The problem is that no 57mm gun... or even 35mm gun like the Gepard achieve their effectiveness by high rate of fire... they simply dont fire fast enough to get enough lead in the air... they have to rely on accuracy for effect and in the case of 57mm guns on guided shells.
23mm Shilka replaced the 57mm gun because the high rate of fire meant 200 shots could be fired at a piece of space in the sky where the target was flying towards. It wasn't super accurate so those 200 shells were scattered in a large cluster... which is a good thing because between the time the rounds are fired and the few seconds until they pass through the air their were aimed at the target could change speed or turn so the fact that they were all over the place just increased the chance of a hit. The higher density just made it less likely the target could fly through the shells and get through without a hit.
The 23mm Shilka was replaced by the Tunguska because the Tunguska had heavier 30mm cannons and a higher rate of fire with two twin barrel guns (5,000 rpm vs 4,000 rpm) and a longer range and heavier HE shell.
The 57mm gun will replace the 30mm calibre guns because it has better range and hitting power but its low rate of fire is compensated by the fact that the rounds will be guided to the target so far fewer rounds will be needed.
Having four barrels is not a help because it does not rely on rate of fire for effect... it relies on guided shells to be effective.
- Surely the system of stabilization of a 57-4 configuration would be done using subsystems for every barrel, that would not be too differents to the system of stabilization that would be used for a 57-1 configuration. Surely for a good stabilization would be required some aditional thing, but my impression is that it would be doable without affect to the rate of fire.
Stabilising four barrels would require a much better stabiliser and the internal space from four guns means less room for ammo and ammo handling systems... a big vehicle might carry 500 rounds, but with four guns it will use up ammo much faster and need to be resupplied more often.
I think a single barrel gun vehicle (note even the navy model of the 57mm gun system shows just one gun so if they don't bother with four I rather doubt the army will bother... even with one gun it will be an effective CIWS replacement being able to hit targets beyond the 4km effective range of the 30mm gatlings).