Not an engineer so what the bleep do I know? Many moons ago I worked in an old beat up truck repair shop. It had a "small" bay that held maybe 4 tractors (as in KW, White Frieghtliner, Peterbuilt) and a jumbo spray booth and a working yard that was maybe an acre where we worked on 40 foot trailers. The shop had two very large industrial air compressors that were simply plumbed into a common 3/4 pipe and ran all thru the shop and out to the acre lot where everybody and his brother used the air. It worked fine (those compressors got one heck of a daily workout.) We used a tremendous amount of electricity too with monster welders all over the place so the juice box was probably enormous.
A sandblasting guy once told me that you can indeed just plug multiple air compressors into a common line and go for it. The more the better he said. Just be prepared for moisture issues and he proceeded to talk me thru the subject of dryers, another subject.
The only caveat would be the power supply for multiple units. In a home, you would need to tap separate circuits with adequate breakers. (probably 20 to 30 amps each depending on the compressor.) Also, extension cords are a no no with air compressors because they act as a resistor and suck up much needed amperage. Short cords. Separate circuits. Should work n'est pas?...