Since we are talking about compressors, I have a tidbit for those who want massive flow at high pressure, well sorta massive flow anyway..
Due to the displacement of the fridge compressor being very small to work with higher pressure and atmospheric pressure is below the normal pressure of the compressor, they are not very efficient and pump quite slow. If you feed a fridge compressor at it's designed inlet pressure, it will output the designed volume at the designed outlet pressure.
If we work from absolute pressures, we can see how to cascade compressors. To make the math easy, I am calling 1 atm 1 unit volume of air in a given volume. A fridge compressor will then take in 1 unit by itself with no boost. Assuming a fridge has an icebox running at about +10 F, the freon (R143a) boils at about 10 PSI or slightly over 1 atm. The freon condenses at above room temperature at a higher pressure often in the 100 to 120 degree range for design outlet pressure of up to 150 PSI.
If we ditch the freezer box and worked with a fridge designed to never make ice you get into air conditioning compressors. Assuming they boil freon on the evaporator (the cold side) at 25 degrees F and the tubing remains above the frost point, we would want an inlet pressure in the range of near 30PSI or +2 units. Note, if the compressor takes in twice as much on each stroke, it delivers twice as much.

Half the pumping time or twice the flow for a BBMG. On the down side, the compressor is now working twice as hard to deliver the output. Keep this in mind. Raising the inlet pressure increases the load.
An advantage of an AC compressor is they are not designed to condense the freon at room temperature

They are designed to dump the heat outside and condense it at outside temperatures. Woo hoo. High pressure baby.
This high pressure, high volume heat pump is why most air conditioners draw way more than a refrigerator. They are bigger!
Back to cascading, several fridge compressors can be used in parallel to feed a single AC compressor's input. I am not sure how many would be needed, but if the fridge compressors were the same displacement as a AC compressor, then 2 compressors in parallel will provide 2 units of air per stroke, but at 2 atm pressure the space occupied would be 1 volume and the A/C compressor would take that volume in each stroke. This would only be a boost of 15 PSI or 1 bar. To boost to 30 PSI or 2 bar, 3 compressors are needed, 3 bar or 4 atm would need 4, etc.
I am assuming an AC compressor being a bigger beast would have a larger displacement, so I would assume that more fridge compressors could be paralleled to feed one A/C compressor. If you do this, then serious considerations need to be given to the electrical requirements.